Hassan Rouhani has been officially sworn in as Iran's new president, promising moderation and transparency but also urging those who want the "right response" from his country to "use the language of respect" instead of sanctions.

In an inauguration ceremony held at the Iranian parliament in Tehran on Sunday, the 64-year-old cleric kissed the Qur'an and took the oath of office before senior politicians, foreign dignitaries and MPs, promising to serve his people, protect individual rights and defend his country.

Rouhani, Iran's seventh president since the 1979 Islamic revolution, formally began his four-year mandate on Saturday when Iran's supreme leader, Ayatollah Ali Khamenei, in a separate ceremony, endorsed his sensational victory in June's presidential election.

During Sunday's swearing-in ceremony, Rouhani delivered a speech in the Majlis (the parliament) in which he said "people have voted for moderation" and that his "government of hope and prudence" would work to fight poverty, corruption and discrimination.

"People want change," said the new president, who described himself as the representative of all Iranian people and not only those who voted for him in the election. "People want to live better, to have dignity as well as a stable life. They also want to recapture their deserving position among nations," he said.

He also pledged to promote women's rights and advance equality for women in society, despite proposing a cabinet of all men. Rouhani said Iranians sought "peace" and "stability" in their region and across the world and said Tehran was against "foreign intervention" in any country. "The only way for interaction with Iran is dialogue on an equal footing, confidence-building and mutual respect as well as reducing antagonism and aggression," Rouhani said. "Transparency is the key to creating trust but it can not be one-sided."

To cheers from MPs, Rouhani added: "If you want the right response, don't speak with Iran in the language of sanctions, speak in the language of respect."

Within hours, the White House extended an olive branch to Rouhani, saying that Tehran would find a "willing partner in the United States" should it choose to engage. The White House also congratulated Iranians "for making their voices heard" during Iran's election.

"We note that President Rouhani recognised his election represented a call by the Iranian people for change, and we hope the new Iranian government will heed the will of the voters by making choices that will lead to a better life for the Iranian people," the White House said.

"The inauguration of President Rouhani presents an opportunity for Iran to act quickly to resolve the international community's deep concerns over Iran's nuclear programme."

It added: "Should this new government choose to engage substantively and seriously to meet its international obligations and find a peaceful solution to this issue, it will find a willing partner in the United States."

At the inauguration ceremony, Rouhani also presented the full list of his cabinet members to the parliament, which included Mohammad Javad Zarif, nominated as the foreign minister. Zarif, a former ambassador to the United Nations, is a US-educated veteran Iranian diplomat who has previously led secret Tehran-Washington negotiations and is seen as best positioned to normalise bilateral relations between the two countries.

But despite the positive signals from both sides, the US house of representatives last week overwhelmingly passed a new sanctions bill that will make existing tough measures against Tehran even more stringent. The bill will come into effect if approved by US senators in September, but a group of senate members have signalled their support for the legislation.

Iran had also invited senior British officials for Rouhani's inauguration. The UK, which has not had a diplomatic presence in Iran since the British embassy in Tehran was attacked by a mob in November 2011, declined the invitation. The foreign office's decision was criticised by the labour party as a "missed opportunity". Despite this, William Hague called his Iranian counterpart last week and said he was willing to meet the Iranian foreign minister during the UN general assembly in New York in September.

Sunday's inauguration was the first of its kind for Tehran, as it was attended by presidents and high-ranking officials from neighbouring countries and around the world. It was broadcast live on state television, with the foreign dignitaries filmed as they arrived in a style resembling the Oscars. The president of Afghanistan, Hamid Karzai, was among at least ten presidents and many prime ministers in the room, though the only western official to attend was Javier Solana, the former EU foreign policy chief.

Also absent was the outgoing president, Mahmoud Ahmadinejad. Ahmadinejad's eight acrimonious years in Tehran's Pastor Street, marred by financial stringency and international isolation because of Tehran's suspected nuclear activities, came to an end on Saturday when he accompanied Rouhani to the presidential offices and handed in the keys before moving to his old house in Narmak, east Tehran.

"We promised to have clean hands; I say with confidence that this government is the cleanest government," Ahmadinejad said during a TV address on Friday before leaving office. "The enemy has introduced heavy sanctions and the nation has faced problems. We have made our utmost effort but we couldn't resolve all the pressures. This issue has been very difficult for us."

In the months before leaving office, Ahmadinejad established a private university, called "Iranian", where he said he would spend his time from now on. Iranians celebrated his departure from power by chanting "Ahmadi Bye Bye" on Saturday night. Former reformist president, Mohammad Khatami, whose endorsement of Rouhani is believed to have played a key role in his success in the election, was apparently not invited for the ceremony. Khatami is accused by hardliners of siding with opposition leaders Mir Hossein Mousavi and Mehdi Karroubi, who have been kept under house arrest for more than two years without being charged or standing trial.

Unlike his predecessor, Rouhani's speech was moderate in tone, carrying no direct reference to the Unites States or Israel.

On Friday, Rouhani was misquoted by an Iranian news agency as saying that Israel was a wound that "should be removed", which prompted Israel's prime minister, Benjamin Netanyahu, to react.

Local agencies admitted their mistake but it was too late for Netanyahu to retract his statement.