Israel's ambassador to the US, Michael Oren, was quoted by Israeli media on Monday as saying that ties between the US and Israel were at their lowest point since 1975.
Asked if that was the case, Mrs Clinton said: "I don't buy that."
She said Washington had an "absolute commitment to Israel's security".
But, she added, the US did not always agree with its international allies on everything, and it had expressed its "dismay and disappointment" to Israel over last week's incident.
Last week, Mrs Clinton called the settlements announcement "insulting" to the US and, in a phone call to Israeli Prime Minister Benjamin Netanyahu, demanded Israel take steps to show its commitment to peace.
The US says it is still awaiting a "formal" response from Israel to those concerns.
Security forces battled protesters in several areas of Jerusalem on Tuesday
Mr Mitchell had been due to meet Israeli President Shimon Peres on Tuesday but the trip has been put off to an as yet undetermined time, officials said.
State department spokesman Philip Crowley said Mr Mitchell would not meet Israeli and Palestinian leaders before a Middle East Quartet meeting in Moscow on Friday but talks would be scheduled at some point.
BBC state department correspondent Kim Ghattas, in Washington, says the pressure is piling up on Israel but the question being asked is whether the US can get anything from Israel at this stage.
It is possible the Israeli prime minister cannot deliver what Washington wants without paying too heavy a price at home, our correspondent says.
Although he has apologised for the timing of the settlement announcement, Mr Netanyahu has stood by Israel's policy, telling parliament on Monday there can be "no curbs" on Jewish building in Jerusalem.
The BBC's Paul Wood in Jerusalem says there seems to be an impasse - if Mr Netanyahu caves in and cancels the new settlements, the stability of his government may be in doubt; if he does not, it is hard to see how the peace talks can take place.
'Day of rage'
Tensions in East Jerusalem have risen in recent days with the settlements issue and the rededication of a synagogue in Jerusalem's Old City, which Palestinians have condemned as provocative. The synagogue was destroyed by Jordanian forces during the war that began in 1948 after the creation of Israel.
This synagogue will be a prelude to violence and religious fanaticism and extremism
Hundreds of Palestinian protesters burned tyres and threw rocks, while police fired stun grenades and tear gas, as rioting broke out in a number of areas - including the Shu'fat refugee camp, al-Eisaweyah and the Qalandia checkpoint between a Palestinian controlled section of the West Bank and a occupied East Jerusalem.
Israeli police said they had deployed 3,000 officers across the city.
The reopening of the twice-destroyed Hurva synagogue, in the Jewish Quarter of the Old City, which Palestinians seek as part of a future capital, triggered a wide backlash.
Hatem Abdel Qader, Jerusalem affairs spokesman for the Fatah movement of Palestinian Authority President Mahmoud Abbas, said: "This synagogue will be a prelude to violence and religious fanaticism and extremism."
Militant group Hamas had declared Tuesday a "day of rage" against the move.
Thousands of people turned out in Gaza to protest against the rededication of the Jerusalem synagogue, which is not far from the al-Aqsa mosque, Islam's third-holiest site, although demonstrations there remained relatively peaceful.
Our correspondent says the call by some Palestinian officials for people to defend the Haram al-Sharif or Temple Mount, site of the al-Aqsa mosque, comes amid rumours of plans by Jewish extremists to take control of the area.
He says that although the clashes so far are small-scale, no-one has forgotten how the last Palestinian intifada - or uprising - began over the holy sites in Jerusalem.
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