The League warned that holding a ballot would obstruct international efforts to resolve the Syrian conflict.
President Bashar al-Assad is expected to make a bid for another seven-year term in office in the June ballot.
The abduction in Tripoli comes two days after Jordan's ambassador to Libya was seized.
Thousands of Muslim Brotherhood supporters have been jailed since the ouster of President Mursi.
New delay comes after a shooting attack in the West Bank, days before negotiations are set to expire.
U.S.-brokered mediations faltered last week when Israel announced plans for new settlement homes.
U.S.-mediated peace talks appeared near collapse this week, as deadline for negotiations nears.
Calls nomination of a former hostage-taker as ambassador to U.N. "extremely troubling."
According to a U.S. official, the newly announced Palestinian reconciliation may affect aid to the region.
Supreme leader said Iran had agreed to the talks to "break the hostile atmosphere."
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