In a statement issued soon afterwards in Ramallah, Mahmoud Abbas, the Palestinian president, accused Israel of breaking international law.
The Palestinian leader called on other countries to end the "unfair" treatment of his people.
Abbas said the Israeli position "completely violates the agreements we have signed with them and violates international law" and demanded that Israel end such measures.
"We say to the Israeli government that we are a peaceful nation but we want our rights," he said.
Speaking in Gaza, Sami Abu Zhuri, a Hamas spokesman, described Israel's decision as "a failed attempt to cause internal divisions among Palestinians".
The Israeli government announced on Sunday that it would cut all contacts with the PA except Abbas - but ruled out full peace talks with him.
The new policy came into immediate effect and a joint Israeli-Palestinian security co-ordination office in Jericho was closed on Monday.
A four-year-old Palestinian girl was killed and 12 others were injured during continued Israeli shelling of the Gaza Strip on Monday.
An Israeli army spokeswoman confirmed that artillery shells had been fired at the area of Beit Lahiya in the northern part of the Gaza Strip, although she did not have details of the specific incident.
"We are very sorry for any innocents who are hurt, but these areas and the courtyards of some of these homes are often used to fire rockets at Israel," she said.