Israel's Prime Minister Benjamin Netanyahu heads home Wednesday with little to show for his attempt to mend a rift with Washington over his efforts to block a nuclear agreement with Iran.

Netanyahu met with US Secretary of State John Kerry before his departure, capping a three-day visit that encompassed his first White House tete-a-tete with US President Barack Obama in a year.

Afterward, Netanyahu said the meeting with Obama on Monday was one of the best he has had with the US president.

"I think we have no disagreement now about what we need to do moving forward," he told an audience at a liberal think tank.

But to observers the meeting was a minimalist diplomatic exercise, a business-like reaffirmation of the two countries close bonds but with no warmth shown by either leader.

"We have a president that treats the prime minister of Israel with less respect than he gives the ayatollah," Senator Marco Rubio remarked during Tuesday night's Republican presidential debate.

Months of bad blood hit a low in March when Netanyahu bypassed Obama to deliver a speech to the Republican-controlled Congress denouncing the nuclear accord as it was being negotiated.

Though embarrassed and angry, the White House brushed off the speech and joined with five other powers in striking the landmark deal with Tehran on July 14.

During his three-day visit to Washington, Netanyahu opened negotiations on US military aid to Israel over the coming decade.

But for now he leaves empty-handed, content to hope that the Americans share Israel's assessment of its security requirements in light of what is happening in the region.

Frank Lowenstein, a Kerry advisor, is traveling to Israel next week to continue talks, the Israelis said. Netanyahu told the Israeli press this week that a US delegation was also expected in Jerusalem in December.

- A message of unity -

Hoarse but speaking impeccable English, the Israeli prime minister has stepped up contacts with Democrats as well as Republicans, hammering a message of "unity" at all his encounters.

In a show of his willingness to improve relations, if not with this US administration then with the next, Netanyahu agreed to a debate at the Center for American Progress, a liberal think tank.

"I came here... because I think it is vital to understand how important it is for me that Israel remain an issue of bipartisan consensus. It's crucial," he said.

But he went on to lay out a particularly pessimistic vision of the Israeli-Palestinian conflict, expressing his view that the current stalemate would remain unchanged, to the disappointment of his audience.

Earlier in the day, he addressed an annual meeting of 4,000 representatives of American Jewish federations, who are traditionally close to the Democrats and have been affected by the controversy over the Iran agreement.

Some representatives of the American Jewish community, the largest in the world with between 4.5 and 5.7 million people, have been accused by their detractors of betraying Israel for having supported the agreement with Iran.

The divisions have revealed, however, that there are limits to American Jewish support for an Israel led by Netanyahu.

"Now, this past year has not been simple. Great issues were debated. Passions ran high," Netanyahu told the meeting. "Maintaining the unity of our people is of paramount importance."