By Tom Perry and Alastair Macdonald

CAIRO, June 21 (Reuters) - Thousands of Islamist supporters of Egypt's President Mohamed Mursi gathered in Cairo after Friday prayers to show support for the elected head of state ahead of protests his opponents hope can force him from office.

Crowds converged on a mosque in the suburb of Nasser City, many waving the national flag, some carrying pictures of the bearded president, in what is intended to demonstrate the Islamists' strength of numbers ahead of opposition rallies set for June 30, the first anniversary of Mursi's inauguration.

"Yes to respecting the will of the people!" read banners.

"There are people seeking a coup against the lawful order," said demonstrator Gaber Nader, 22, his head protected from the burning early afternoon sun by a green banner from Mursi's Muslim Brotherhood, the movement whose organisational strength won it successive elections since the fall of Hosni Mubarak.

"Dr. Mursi won in free and fair elections like in any state in the world," Nader said, shrugging off concerns among the less well organised opposition that the Brotherhood is aiming for a monopoly of power and to install Islamic rule and social order.

"The secular parties are eating the democracy that God gave them," he added. "The secularists are not respecting democracy."

Secular groups say they have gathered some 13 million signatures - almost equal to the number of votes that elected Mursi a year ago - on a petition calling on him to step down.

They plan mass rallies across Egypt on June 30 and have attracted support from many Egyptians less politically motivated but exasperated by economic stagnation under Mursi and the Islamist-led legislature.

Reflecting a sense their electoral success is under siege from unelected institutions and vested interests rooted in the Mubarak-era, when their party was banned, some in Friday's crowd - mostly men, with a few women, heavily veiled - chanted for "A purge of the judiciary!" and "A purge of the media!"

There was no trouble evident around the crowd of well over 10,000 in Cairo, but state newspaper al-Ahram carried a report on its website from the second city of Alexandria saying there had been some violence between pro- and anti-Mursi factions.

OPPOSITION FRUSTRATION

Opposition groups range from the young liberals who first took to Tahrir Square in January 2011 to challenge Mubarak, to conservatives yearning for the stability of army rule. Many in Egypt's 10-percent Christian minority also fear the Islamists.

Mohamed ElBaradei, the former top U.N. diplomat who is a leader of the opposition "Rebel!" campaign, told Al-Hayat newspaper that economic problems, including power cuts as summer heat takes hold, were fuelling support for a movement which he said hoped to end the "total polarisation in Egypt".

ElBaradei said a united opposition push could bring an early presidential election that would unseat Mursi, though he himself would not run: "The division of the opposition put Mursi in power and I believe it has realised this mistake," he said.

Tensions between Mursi's supporters and opponents spilled over into violence outside Cairo this week. Around 100 people have been injured in scattered skirmishes triggered by Mursi's decision to appoint more Islamists as provincial governors.

Rhetoric has grown more toxic in recent days: one Islamist cleric referred to Mursi's opponents as "infidels" during a rally attended by the president last week. The opposition are billing it as Mursi's last days in office, hoping for a repeat of the uprising that toppled Mubarak two and half years ago.

But Egypt's biggest Salafi Islamist force, the Nour Party, is not taking part. It warns of "an imminent collision" between Egyptians and called on both sides to give ground - Mursi by appointing a cabinet for national unity and the opposition by switching its focus to elections from street protests. (Additional reporting by Shadia Nasralla, writing by Alastair Macdonald)