STRASBOURG, July 6 (Reuters) - The European Parliament on Thursday asked for Turkey's European Union accession talks to be suspended if Ankara implements a constitutional overhaul, backed by a referendum in April, which expands the powers of President Tayyip Erdogan.

The parliament has limited influence on the issue and Turkey said on Thursday it rejected proposals that it drop its EU membership bid in favour of cooperation in other areas.

EU leaders have been critical of Erdogan and his behaviour toward opponents, both before and after an abortive coup against him a year ago. But they do not want to undermine an agreement struck last year whereby Turkey effectively stopped migrants reaching Greece, easing a crisis that had threatened EU unity.

The resolution passed by the parliament on Thursday "calls on the Commission and the member states, in accordance with the Negotiating Framework, to formally suspend the accession negotiations with Turkey without delay if the constitutional reform package is implemented unchanged."

Erdogan's proposed constitution would greatly expand his powers, which he says is necessary to ensure stability in Turkey.

Opposition parties and human rights groups say the reforms threaten judicial independence and push Turkey towards one-man rule. The EU has also expressed concern.

The Venice Commission, a panel of legal experts from the Council of Europe, a rights body to which Turkey belongs, warned in March ahead of Turkey's referendum that the proposed constitutional shakeup represented a "dangerous step backwards" for democracy. Ankara rejected the criticism.

(Reporting by Julia Fioretti in Brussels; editing by Andrew Roche) ((julia.fioretti@thomsonreuters.com; +32 2287 6875; Reuters Messaging: julia.fioretti.thomsonreuters.com@reuters.net))