By Arshad Mohammed

WASHINGTON (Reuters) - Egypt summoned the U.S. ambassador in Cairo to show displeasure at Muslim Brotherhood figures coming to Washington for a private conference, sources familiar with the matter said on Monday.

One source, who spoke on condition of anonymity, said U.S. officials did not intend to meet the group although they had met some Brotherhood figures that came to Washington in January.

The tensions reflect a clash between U.S. diplomats' desire to deal with the whole political spectrum in Egypt and a fear of alienating Egyptian President Abdel Fattah al-Sisi who, as army chief, toppled a Muslim Brotherhood-led government in 2013.

The sources declined to say precisely when U.S. Ambassador Stephen Beecroft was call in by the Egyptian government, though one said it was in recent days. Egypt sought the meeting to make clear its unhappiness at U.S. dealings with the Brotherhood.

State Department spokesman Jeff Rathke declined to say whether Beecroft was summoned by the Egyptian authorities or whether U.S. officials would meet Brotherhood figures visiting Washington, telling reporters he was aware of media reports of such a visit but that "I don’t have any meetings to announce."

He said it continued to be U.S. policy to engage with people from across the political spectrum in Egypt.

The United States has had ambivalent dealings with Sisi, prizing the stability has brought to Egypt while cautiously criticizing Egypt's human rights record and the authorities' crackdown on the Brotherhood.

Sisi, who was elected president in a 2014 landslide but with lower-than-expected turnout that raised questions about his mandate, regards the Brotherhood as part of a terrorist network that poses a threat to the Arab and Western world.

The Brotherhood says it is a peaceful movement.

The fall of veteran autocrat Hosni Mubarak in 2011, a long-time U.S. ally ultimately abandoned by Washington, paved the way for the Brotherhood to rule the most populous Arab country, something that was unthinkable for decades.

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Mohamed Mursi, who rose through the Brotherhood's ranks before winning the presidency in 2012, was a polarizing figure during his troubled year in office. His policies alienated secular and liberal Egyptians, who feared the Brotherhood was abusing power.

In January, the State Department said its officials met a group of visiting Egyptian former parliamentarians, including former members of the Freedom and Justice Party, the Brotherhood's political wing. The Brotherhood was banned by an Egyptian court in 2013 after Mursi was ousted.

(Additional reporting by Stephen Kalin, Yara Bayoumy and Shadi Bushra in Cairo; Reporting by Arshad Mohammed; Editing by Lisa Shumaker)