GAZA, Sept 19 (Reuters) - Hamas sharply criticised the arrest of dozens of its members by Palestinian Authority police in the West Bank on Wednesday, underscoring dire relations between the Islamist group and its Fatah-dominated rival after a failed bid for reconciliation.

President Mahmoud Abbas' Western-backed Palestinian Authority denied any political motives behind the round-up, which saw as many as 71 people detained, and said it had targeted criminals and that many were freed after questioning.

The detentions came at a time of renewed friction between Hamas, which controls the Gaza Strip, and Abbas, who holds sway in the occupied West Bank.

West Bank officials say Abbas is particularly upset at the developing ties between the Hamas leadership and the new authorities in Egypt. A delegation from Gaza met Egyptian Prime Minister Hisham Kandil in Cairo on Monday.

Hamas seized control of Gaza in a brief civil war in 2007. Abbas still claims to represent all Palestinians, but has not set foot in Gaza since his faction was ousted and the two sides regularly accuse each other of judicial harassment.

"Everyday, Abbas surprises us, confirming that he is harming our people and our parties," said senior Hamas lawmaker Ismail Al-Ashqar, after news of the West Bank arrests.

He urged fellow Palestinians to "reject" Abbas and to "bring him before justice for his anti-national deeds".

The Palestinian Center for Human Rights said 71 Hamas supporters had been detained in the past 24 hours.

Adnan Dmeiri, spokesman for the security services loyal to Abbas, told Reuters the number was exaggerated, but did not offer any alternative figures.

"Arrests were made all over the West Bank in a legal fashion, involving cases of possession of weapons, incitement, money-laundering and attempts to transfer the Gaza takeover into the West Bank," he said.

Abbas and Hamas announced they were ready to lay aside their differences in 2011 and overcome the divisions that have led to a near total schism between the West Bank and Gaza.

The split is widely denounced by ordinary Palestinians, but all efforts to make good on last year's accord have foundered, including an attempt by the new Islamist leaders in Cairo to broker a deal between the two sides.

Abbas's allies fear Cairo is ready to side with Hamas, which could ultimately damage their own standing elsewhere in the Arab world. They looked on with concern as the Egypt's prime minister held talks on Monday with Hamas's Gazan leader, Ismail Haniyeh.

"Holding economic, political and security talks with Ismail Haniyeh sends a wrong message to the Hamas leadership in Gaza, encouraging it to continue neglecting Palestinian reconciliation," said Palestine Liberation Organisation (PLO) senior member Saleh Raafat. The Fatah-dominated PLO has been recognised by the U.N. as the Palestinians' sole representative abroad for almost four decades.

In an effort to regain the political initiative, Abbas is due to address the United Nations next week and seek recognition of a Palestinian state as a non-member of the U.N. - the sort of status already granted to the Vatican City.

Hamas, which refuses to recognise Israel's right to exist, has dismissed such diplomatic moves as a waste of time. (Additional reporting by Jihan Abdalla in Ramallah; Editing by Louise Ireland)