On Monday, Obama held talks with Netanyahu and told the Israeli PM to stop expanding Jewish settlements and grasp the "historic opportunity" to make peace with the Palestinians.
In an interview with Al Jazeera, Clinton said the Obama administration is "determined to forge ahead on what we believe is in the best interest of the Israelis, the Palestinians, the larger region, and the world as well as what we think is right".
Clinton said the US was pursuing "a two-step effort".
"First, we want to see a stop to settlement construction - additions, natural growth, any kind of settlement activity - that is what the president has called for.
"We also are going to be pushing for a two-state solution which by its very name implies borders that have to be agreed to and we expect to see two states living side-by-side," she said.
The settlements issue was also raised by John Kerry, a high-profile senator, with Netanyahu during his visit to the US congress on Tuesday.
Kerry, who chairs the senate foreign relations committee, stressed "the importance of Israel moving forward, especially in respect to the settlements issue".
But he said the issue was not "a one-way street" and that Arab steps towards joining the "regional road map" to peace were also critical.
The Palestinians say settlements, which the UN has deemed illegal, could deny them a viable state.
After meeting Kerry, Netanyahu said he wanted to renew the Palestinian peace process "immediately", in tandem with an effort to gain backing from Arab states for efforts to counter Iran's nuclear ambitions.
"We have a unique historical circumstance in that Israel and many of our Arab neighbours understand the threat posed by Iran's quest to develop nuclear weapons capabilities," Netanyahu said.
"We intend to pursue the peace track independently of what happens in Iran, but in point of fact ... it should be done in parallel."
|Obama, right, told Netanyahu on Monday to halt settlements [EPA]
Netanyahu's visit has brought to the fore differences between the US and Israel over Iran and the Middle East peace process.
However, Netanyahu told Nancy Pelosi, the Democratic house speaker, and John Boehner, the Republican house minority leader, that he saw "an American consensus" regarding "the special relationship we have between Israel and the United States".
"We face opportunities and [a] challenge. The challenge is the potential arming of Iran with nuclear weapons capabilities. That is a great danger to all of us," Netanyahu said.
"I was assured by President Obama yesterday [Monday] that the US is committed to preventing that from happening."
Obama said he was ready to seek deeper international sanctions against Iran if it shunned US attempts to open negotiations on its nuclear programme.
The US leader said he expected a positive response to his diplomatic outreach by the end of the year.
Manouchehr Mottaki, Iran's foreign minister, reiterated on Tuesday that Tehran appreciates Obama's new approach but is waiting for concrete changes in US policy.