Facing fierce resistance from the White House and medical experts to a strict new mandatory quarantine policy, Gov. Andrew M. Cuomo said Sunday night that medical workers who had contact with Ebola patients in West Africa but did not show symptoms of the disease would be allowed to remain at home and would receive compensation for lost income.

Mr. Cuomo’s decision capped a frenzied weekend of behind-the-scenes pleas from administration officials, who urged him and Gov. Chris Christie of New Jersey to reconsider the mandatory quarantine they had announced on Friday. Aides to President Obama also asked other governors and mayors to follow a policy based on science, seeking to stem a steady movement toward more stringent measures in recent days at the state level.

The announcement by Mr. Cuomo seemed intended to draw a sharp contrast — both in tone and in fact — to the policy’s implementation in New Jersey, where a nurse from Maine who arrived Friday from Sierra Leone was swiftly quarantined in a tent set up inside a Newark hospital, with a portable toilet but with no shower.

It was the second striking shift in Mr. Cuomo’s public posture on the Ebola crisis in 72 hours; after urging calm on Thursday night, then joining Mr. Christie to highlight the risks of lax policy on Friday, Mr. Cuomo on Sunday night appeared to try to dial back his rhetoric and stake out a middle ground.

He said his decision balanced public safety with the need to avoid deterring medical professionals from volunteering in West Africa. “My No. 1 job is to protect the people of New York, and this does that,” he said. Those quarantined at home will be visited twice a day by local authorities, he said. Family members will be allowed to stay, and friends may visit with the approval of health officials.

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