Seven people were killed and 261 left wounded in Cairo when supporters of Mohamed Morsi clashed with the deposed president's opponents and security forces overnight, the head of Egypt's emergency services said on Tuesday.

Mohamed Sultan said two people had been killed at a bridge in central Cairo and five more in the capital's Giza district.

Egyptian authorities arrested 401 people over the fighting overnight, nearly two weeks after the army removed Morsi in response to mass demonstrations against him.

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Meanwhile, a senior official in Egypt's Muslim Brotherhood said on Tuesday that interim Prime Minister Hazem el-Beblawi had not offered the movement any posts in the transitional cabinet, and that if he did, the Brotherhood would reject it.

“Beblawi, or anyone from the government of the coup, did not offer us any position in the government, and if they do, we will refuse,” Mohamed El-Beltagi told reporters.

Interim Prime Minister Hazem el-Beblawi is forming a government to lead Egypt through a “road map” to restore full civilian rule and to tackle a chaotic economy, although a new minister said aid from Arab states meant Cairo did not need to resume talks on a long-delayed IMF loan.

Egyptian police clashed with protesters after fights broke out between supporters of the president and locals angered when they tried to block major thoroughfares crossing the River Nile.

Young men covered their mouths as police fired tear gas, throwing stones at them and shouting pro-Morsi and anti-military slogans, as well as “Allahu Akbar!” (God is greatest).

Military helicopters hovered overhead whilst police vans were brought in to quell the trouble, before dozens of riot police were dispatched. Medics attended to men with deep gashes to their eyes and faces.

The clashes came as the US has tried to reduce the mistrust Egyptians feel towards the American government. On a visit to Egypt yesterday, the US Deputy Secretary of State William Burns told reporters in Cairo that Washington had no desire to meddle in Egypt, which it supports with $1.5 billion in aid each year, most of which goes to the military.

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“Only Egyptians can determine their future,” Burns told reporters at the US embassy. “I did not come with American solutions. Nor did I come to lecture anyone. We will not try to impose our model on Egypt.”

Washington has so far refused to say whether it views Morsi's removal as a coup, which would require it to halt aid.

The Islamist Nour Party and the Tamarud anti-Morsi protest movement both said they turned down invitations to meet Burns.

But a senior State Department official denied Burns had been shunned. “I don't think we're losing influence at all,” the US official said, adding that Burns was still in Cairo.

“I don't know what meetings he has, but he has seen a range of people in Cairo in the interim government, in civil society ... so it's hard to say he has been spurned by both sides. I don't accept that is the case.”

Frustrations echoed those of millions of Egyptians who rallied for Morsi's resignation on 30 June. The military said it deposed him to fulfil the wishes of the people, but the Muslim Brotherhood movement described it as a coup.

“It's the army against the people, these are our soldiers, we have no weapons,” said Alaa el-Din, a 34-year-old computer engineer. “The army is killing our brothers, you are meant to defend me and you are attacking me. The army turned against the Egyptian people.”

Tens of thousands of Brotherhood supporters gathered late on Monday at the Rabaa Adawiya mosque in northeastern Cairo, where they have staged a sit-in vigil for the last three weeks vowing to remain until Morsi is reinstated.

Another large crowd rallied outside Cairo University, and there were protests in the coastal city of Alexandria and the Nile city of Assiut. There also were minor clashes in Giza, home of the pyramids, just outside Cairo.

The army warned demonstrators that it would respond with “the utmost severity and firmness and force” if they approached military bases or “vital state institutes.”

At least 92 people were killed in the days after Morsi was toppled, more than half of them shot by troops outside the Republican Guard compound near the Rabaa mosque on 8 July. Protests since then have been tense but peaceful - until Monday night.

The political turmoil and unrest in major cities has also fuelled violence in Egypt's lawless North Sinai province bordering Israel and the Palestinian Gaza Strip.

Attacks in the area have killed 13 people, mainly police, since 3July. In the most recent, suspected Islamist militants fired grenades at a bus carrying workers from a factory in the Sinai city of El Arish on Monday, killing three and wounding 17.

Morsi is being held incommunicado at an undisclosed location. He has not been charged with a crime but the authorities say they are investigating him over complaints of inciting violence, spying and wrecking the economy. Scores of Morsi supporters were rounded up after violence last week.

Many of the top Brotherhood figures have been charged with inciting violence, but have not been arrested and are still at large. The Public Prosecutors' office announced new charges against seven Brotherhood and Islamist leaders on Monday.

Burns had earlier called for restraint from both sides. “If representatives of some of the largest parties in Egypt are detained or excluded, how are dialogue and participation possible?” he asked. He also urged those opposed to Morsi's ouster to participate in the political process peacefully.

Additional reporting by agencies