When Israeli premier Benjamin Netanyahu took up a job in the private sector on being voted out of office in 1999, one 56-year-old US senator kept in touch.

The senator was Joe Biden, and the correspondence helped sustain ties that have lasted for years. As president of the US, Israel’s main ally, he is in a stronger position than any other foreign leader to influence the course of this month’s deadly resurgence of fighting between Israel and the Palestinian militant group Hamas in the Gaza Strip.

After initially endorsing air strikes by Washington’s closest regional ally, Biden has begun to toughen his line during regular calls with Netanyahu as attacks continued into a second week.

While speculation grew on Thursday that a ceasefire could be agreed in the coming days, Israel continued to launch strikes against Hamas. After Biden told Netanyahu on Wednesday that he expected de-escalation, the Israeli prime minister said he was “determined to continue this operation until its aim is met”.

Biden is now facing a mounting political backlash at home as the death toll rises, including accusations from some in his own political party that he is enabling Netanyahu.

At least 230 Palestinians, including 104 women and children, have been killed since the conflict began on May 10, according to Gaza health officials. Twelve Israelis have been killed, including two children. The ties between the two men are under a spotlight.

After Biden took office, there was much speculation about whether he would take a tougher stance towards Israel than his predecessor Donald Trump, who pursued unabashedly pro-Israeli policies, infuriating and sidelining the Palestinians as he upended years of US convention and developed a cosy relationship with Netanyahu.

Biden has recalled first becoming “close friends” with Netanyahu in 1982 when he was posted to Washington as an Israeli diplomat. In those early days, Biden even signed a picture for the young Netanyahu with the words: “Bibi, I don’t agree with a damn thing you say, but I love you.”

During the Obama administration, a fractious period for US-Israeli relations, the then-US vice-president was called in to smooth over ruptures, said Dennis Ross, a former Middle East negotiator. In 2010, after Israel infuriated the White House with its ambition to expand its settlements programme in the occupied West Bank, Ross said he heard Biden speak to Netanyahu with an easy familiarity.

“‘Listen, old buddy, we gotta find a way out of this’,” Ross recalls Biden telling the Israeli prime minister. “It just cast it in a different light.”

Yet in 2015, during another period of friction over Iran policy, Biden conspicuously failed to attend an address Netanyahu gave to a joint session of US Congress.

Michael Oren, former Israeli ambassador to the US during the Obama administration, said the pair had a rapport and could talk “candidly” to one another, but he warned against overstating their warmth.

“It’s not that they were drinking buddies, they saw each other occasionally and had a cordial, good relationship,” he said.

Some observers suggest that Biden’s connection allows him to deliver blunt messages with a soft edge. “Biden is willing to push harder with those he already has a relationship with,” Ross said.

Robert Satloff, executive director of the Washington Institute for Near East Policy, a think-tank, said Biden had seen how putting pressure on Netanyahu in public could backfire. Barack Obama’s decision to press for a ceasefire early and publicly during a similar 2014 conflict between Israel and Hamas quickly made him “an irrelevant factor” and the war continued for 52 days, with more than 2,000 Palestinians and 73 Israelis dead, he said.

“I think the president, by not projecting the level of sympathy and understanding for Israel’s predicament, sort of negotiated himself out of being an effective player in bringing about the end of the conflict,” he said. “What we’re seeing now is a different approach by this administration. Early on they decided publicly, they’re going to be very supportive and sympathetic . . . with considerable private discussions all along.”

The Biden administration has several times blocked statements from the UN security council about this month’s violence. Some analysts argue the fact that Israel has continued with air strikes gives little indication that Biden has privately leaned on Netanyahu to stop.

Biden visited Israel a few months after becoming a US senator in 1973, meeting Prime Minister Golda Meir on the eve of the Yom Kippur war in what he has described as “one of the most consequential meetings” of his life. He recalled her saying that Israelis had a secret weapon in their conflict with the Arabs: “We have nowhere else to go.”

Aaron David Miller, a former Arab-Israeli negotiator in several US administrations, said Biden’s support for Israel was unwavering, but his relationship to Netanyahu was between one politician and another.

“They don’t trust each other,” Miller said. “Biden is very much aware that Netanyahu is a politician; that his primary objective is to maintain himself in power.”

For his part, Netanyahu also understands Biden cannot afford to overlook powerful domestic politics in the US, said analysts based in Washington. This week he expressed support for a ceasefire and immediate de-escalation after receiving criticism from progressive Democrats and some in the pro-Israel lobby in the US.

Although Israel still draws strong bipartisan support in the US, a quarter of Americans now sympathise more with Palestinians than Israelis, up from 16 per cent in 2001, according to Gallup. Only a third of Democrats in 2008 thought the US should pressure Israelis to make compromises rather than Palestinians, but now that figure is 53 per cent.

Biden has begun to acknowledge losses suffered by Palestinians. On Tuesday he told Rashida Tlaib, a progressive congresswoman and vociferous critic of his policies on Israel, that he admired her concern for others and would keep her family in the West Bank safe.

However, Satloff argued Biden’s publicly supportive approach to Israel was more likely to bring an end to fighting. “My sense is that having that position has provided the administration with more standing to be effective in bringing about a halt to the conflict,” he said. “Whether it’s going to happen tomorrow or this hour or that hour, it’s not going to be 52 days long.”