"I think a failure to reach a settlement after so many efforts would benefit no-one," Raab said after talks with his Cypriot counterpart Nikos Christodoulides.
Raab's remarks come two days after Turkish Foreign Minister Mevlut Cavusoglu said any Cyprus peace deal in line with the long-established, UN-backed formula of federation is off the table after decades of fruitless talks, and any accord should be negotiated between two equal sovereign states.
Greek Cypriots strongly reject any deal that would legitimize the island nation's division along ethnic lines.
Since Turkey invaded in 1974, the island, including its capital Nicosia, has been divided with the Turkish-Cypriots congregating in the north where there is a large Turkish military presence.
Mr Raab met with the Turkish-cypriot leader Ersin Tatar who reiterate Turkey's position for a two - state solution along current ethnic lines rather than a federated state which is the preferred position of the Cypriot government.
Mr Christodoulides said any peace deal must be in line with UN resolutions and EU law.