* Mohamed Ali Bishr accused of calling for mass protests

* Former minister has pressed for Mursi's reinstatement

CAIRO, Nov 20 (Reuters) - Egyptian police on Thursday arrested Mohamed Ali Bishr, one of the few Muslim Brotherhood leaders to escape jail after last year's overthrow of Islamist President Mohamed Mursi, in the latest sign of a crackdown on political dissent.

Bishr, a veteran politician who served as a cabinet minister under Mursi, was accused of calling for mass protests on Nov. 28, state media said.

Since the army toppled Mursi in July 2013, Egypt has banned the Brotherhood, its oldest Islamist movement, labelled it a terrorist organisation and rounded up thousands of its members.

With much of the leadership, including Mursi, in jail, Bishr had played a key role in keeping the group's activities alive underground. He was also involved in a pressure group that had pushed for Mursi's reinstatement and was banned last month.

The group, the National Coalition to Support Legitimacy and Reject the Coup, condemned Bishr's arrest, which came a day after 25 protesters were detained in downtown Cairo.

"We reject the continuation of rabid attacks against components of the coalition and its members... and against the sons and daughters of the student protest movement," the group said on its Facebook page.

The outlawed Freedom and Justice Party, the political wing of the Brotherhood, condemned the arrest and said Bishr had served seven years in jail from 1999-2002 and from 2006-2010.

Once among Egypt's best-organised and most successful political movements, the Brotherhood won the first parliamentary and presidential elections after the 2011 Tahrir Square revolution that toppled veteran autocrat Hosni Mubarak.

Mursi ruled for a year, but angered many Egyptians by giving himself sweeping powers and mismanaging the economy, prompting mass protests against his rule.

Abdel Fattah al-Sisi, the army chief behind Mursi's removal, went on to win a presidential election in May and vowed that the Brotherhood would cease to exist under his rule. The organisation says it is a peaceful movement. (Reporting by Omar Fahmy and Shadi Bushra, editing by Lin Noueihed and Mark Trevelyan)