By Arshad Mohammed and Marwa Awad

CAIRO, July 15 (Reuters) - Protesters threw tomatoes and shoes at U.S. Secretary of State Hillary Clinton's motorcade on Sunday during her first visit to Egypt since the election of Islamist President Mohamed Mursi.

A tomato struck an Egyptian official in the face, and shoes and a water bottle landed near the armoured cars carrying Clinton's delegation in the port city of Alexandria.

A senior state department official said that neither Clinton nor her vehicle, which were around the corner from the incident, were struck by any of the projectiles.

Protesters chanted: "Monica, Monica", a reference to Former President Bill Clinton's extra-marital affair. Some chanted: "leave, Clinton", Egyptian security officials said.

It was not clear who the protesters were or what political affiliations they had. Protesters outside Clinton's hotel on Saturday night chanted anti-Islamist slogans, accusing the United States of backing the Muslim Brotherhood's rise to power.

The assault on her motorcade came on a day Clinton spoke at the newly re-opened U.S. consulate in Alexandria, addressing accusations the United States, which had long supported former President Hosni Mubarak, of backing one faction or another in Egypt following his ouster last year.

"I want to be clear that the United States is not in the business, in Egypt, of choosing winners and losers, even if we could, which of course we cannot," Clinton said.

Clinton also met the country's top general, Field Marshal Hussein Tantawi, on Sunday to discuss Egypt's turbulent democratic transition as the military wrestles for influence with the new president.

RIGHTS OF ALL

The meeting came a day after she met Mursi, whose powers were clipped by the military days before he took office.

Mursi fired back by reinstating the Islamist-dominated parliament that the army leadership had disbanded after a court declared it void, deepening the stand-off before the new leader even had time to form a government.

The result has been acute political uncertainty as the various power centres try to find a way to get along in a country that still has no permanent constitution, parliament or government more than a year after Mubarak's downfall.

In their hour-long meeting, Clinton and Tantawi discussed Egypt's political transition and the military's "ongoing dialogue with President Mursi," a U.S. official travelling with Clinton said in an email brief.

"Tantawi stressed that this is what Egyptians need most now - help getting the economy back on track," the official said.

Clinton "stressed the importance of protecting the rights of all Egyptians, including women and minorities".

The talks also touched on the increasingly lawless Sinai region and the Israeli-Palestinian peace process.

Speaking after the meeting, Tantawi said the army respected the presidency but would not be deterred from its role of "protecting" Egypt.

"The armed forces and the army council respects legislative and executive authorities," he said in a speech to troops in the city of Ismailia. "The armed forces would not allow anyone to discourage it from its role in protecting Egypt and its people."

TIES STRAINED

Ties with the United States, which provides Egypt with an annual $1.3 billion in military aid, were strained this year when Egyptian judicial police raided the offices of several U.S.-backed non-governmental organisations on suspicion of illegal foreign funding and put several Americans on trial.

The spat ended when Egyptian authorities allowed the U.S. citizens and other foreign workers to leave the country.

During her speech, Clinton said: "When we talk about supporting democracy, we mean real democracy."

"To us real democracy means that every citizen has the right to live, work and worship as they choose, whether they are man or woman, Christian or Muslim."

"Real democracy means that no group or faction or leader can impose their will, their ideology, their religion, their desires on anyone else."

That was a message she is likely to have repeated in meetings on Sunday with women and Christians, both groups that fear their rights may be curtailed under a Muslim Brotherhood-dominated government.

"She wanted, in very, very clear terms, particularly with the Christian group this morning, to dispel that notion and to make clear that only Egyptians can choose their leaders, that we have not supported any candidate, any party, and we will not," a senior U.S. official told reporters. (Editing by Robin Pomeroy)

Copyright 2012 Thomson Reuters. Click for Restrictions.