Foreign Secretary William Hague says the UK has been asked by the Egyptian government to freeze the assets of some of its former officials.
He told MPs that the UK authorities would take swift action against any illegal activity.
Mr Hague later commented on reports of attacks on protests in Iran, urging the authorities to protect free expression.
He urged the Iranian authorities to "ensure that the security authorities exercise restraint".
While addressing MPs, Mr Hague welcomed the promise of the Egyptian military to establish a democratic government.
The foreign secretary said there was now "a precious moment of opportunity" both in Egypt and Tunisia.
In a wide-ranging statement to the Commons, Mr Hague called for a timetable for free and fair parliamentary elections in Egypt.
He pointed out that Egypt is a sovereign country: "We must not seek to dictate who runs its affairs.
Asset freezing request
"But we have been clear throughout the process that it is in our national interest as well as theirs for them to make a successful transition to a broad based government."
And he called for the release of those detained during the demonstrations: "The United Kingdom must always uphold the right of peaceful protest and freedom of speech."
Mr Hague then revealed that the UK government had received a request from the Egyptians to freeze the assets of several of the country's former officials.
He stopped short of naming any individuals, and explained that the UK would work with other European and international partners on asset freezing.
"We will of course co-operate with this request. If there is any evidence of illegality or misuse of state assets we will take firm and prompt action."
Chancellor George Osborne will raise the issue in meetings with other European finance ministers in meetings later and on Tuesday, he said.
This would be alongside discussions about financial support for Egypt and Tunisia.
Mr Hague's statement to MPs also covered other areas in the Middle East.
There is a risk, he said, that governments would draw what he called the "wrong conclusions" from events and "pull back" from efforts to restart the peace process between Israelis and Palestinians.
"We need to see an urgent return to talks so that legitimate aspirations for two states can be fulfilled through negotiations."
The foreign secretary went on to call the attention of MPs to Iran and what he called "the grave danger of its nuclear programme".
The Iranians had not made meaningful concessions in recent talks, he said.
"We are now in talks with international partners about steps to increase the legitimate peaceful pressure on Iran."
Later, amid reports of protests in Iran, Mr Hague issued a statement in which he said he had seen reports of "peaceful demonstrators being assaulted by Iranian security forces".
He said: "President Ahmadinejad last Friday told the Egyptian people that they had the right to express their own views about their country.
"I call on the Iranian authorities to allow their own people the same right and to ensure that the security authorities exercise restraint."