JERUSALEM, June 15 (Reuters) - Israel has tightened rules for Palestinian staff of the United Nations who travel in and out of the occupied West Bank, increasing tensions with the world body, internal U.N. emails and aid workers said on Sunday.

The Israeli army informed U.N. officials in Jerusalem that Palestinians using the main checkpoint for the West Bank city of Ramallah were required to cross on foot through a terminal for inspection rather than drive through in their U.N. vehicles, a U.N. email said.

The message, sent to employees last week and obtained by Reuters on Sunday, directed Palestinian staff members to use another crossing.

U.N. Palestinian staff have also been asked at three checkpoints to sign a form used by police in conducting searches and making arrests. Another internal U.N. email told staff not to sign the form.

Israeli officials had no immediate comment.

An aid worker said the tightened restrictions had "ratcheted up tensions between Israel and the NGO (non-governmental organisation) community".

U.S. Secretary of State Condoleezza Rice, who is visiting Israel and the West Bank this week, criticised Israel for not doing enough to ease restrictions on Palestinians in the West Bank.

Several thousand Palestinians work for U.N. agencies in the West Bank. Thousands more work in the Hamas-controlled Gaza Strip. (Reporting by Adam Entous; Editing by Catherine Evans)