Israel's prime minister, Binyamin Netanyahu, tried to smooth over a breach in relations with the US today, speaking out against unnamed confidants who described Barack Obama as pro-Palestinian and Israel's "greatest disaster".

Netanyahu made his first public comments after a fraught visit to Washington last week, where he held a long but low-key meeting with Obama that ended with significant disagreement.

Israeli reports said the US was pressing Israel to freeze settlement construction in East Jerusalem and to extend a temporary, partial curb on West Bank settlement building. But so far Netanyahu has shown no sign that he will bow to pressure from Washington. One of his most senior cabinet ministers was reported today as saying the US demands were unacceptable and there would be no compromise.

The Yedioth Ahronoth, an Israeli newspaper, sparked the premier's anger when it quoted unnamed Netanyahu confidants delivering extraordinary criticisms of the US administration. One said Obama and Hillary Clinton, the secretary of state, had "adopted a patently Palestinian line".

"We're talking about something that is diseased and insane," the confidant told the paper. "The situation is catastrophic. We have a problem with a very, very hostile administration. There's never been anything like this before. This president wants to establish the Palestinian state and he wants to give them Jerusalem … You could say Obama is the greatest disaster for Israel, a strategic disaster."

Netanyahu admitted to his cabinet this morning that after his meetings with Obama, although there were some agreements, "there are matters that we have yet to agree on". But he singled out the comments in the Yedioth as "anonymous, unworthy remarks". "Relations between Israel and the US are those between allies and friends and reflect long-standing tradition," Netanyahu said.

In the US, there was a similar effort to ease the rift. David Axelrod, a senior Obama adviser, said the US had a "deep, abiding interest in Israel's security". Despite the low-key nature of the meeting with Netanyahu which ended without a joint statement or customary photographed handshake, Axelrod told CNN: "There was no snub intended. This was a working meeting among friends."

Washington spent much of last year trying to persuade Netanyahu to halt all settlement construction as a prelude to restarting peace talks with the Palestinians for the first time since Israel's war in Gaza. However, Netanyahu agreed only to a partial, 10-month curb of settlement building in the West Bank. That brought initial US praise, but the dispute erupted again earlier this month when Israeli officials approved 1,600 new settler homes in East Jerusalem during a visit by the US vice-president, Joe Biden. That scuppered a programme of indirect talks between Israel and the Palestinians that Washington had spent months arranging.

Israel claims sovereignty over East Jerusalem, which it captured in 1967, but that is not recognised by the international community. Britain, and many others, regard the east of the city as under military occupation, like the West Bank. Settlement on occupied land is illegal under international law.

The Yedioth Ahronoth also quoted one unnamed senior Israeli minister, from the forum of seven top ministers, as strongly rejecting the US demands. "Our decision on this matter is not to give in, not to compromise and not to accept their list of demands," the minister said. "The document of demands that the Americans submitted to Netanyahu in the White House is unacceptable."

Netanyahu met with his senior ministers today and will hold more meetings this week. Reports said some wanted to work with the US to resume peace talks, but other more rightwing ministers were against a halt to settlement building in Jerusalem or any discussion of the future of Jerusalem during indirect talks. The latter included Avigdor Lieberman, the foreign minister, Moshe Ya'alon, the vice-prime minister, Eli Yishai, the interior minister, and Benny Begin, a minister without portfolio.

Like other Israeli prime ministers before him, Netanyahu has to balance pressure from the US with pressure from within his rightwing coalition. Some Labour party ministers from within the coalition have now threatened to quit. They want two key rightwing parties to be forced out of government and replaced with Kadima, the centrist party led by Tzipi Livni which polled first in elections last year.