Instead, they say she must search her heart for the best solution.
A carefully-worded statement - drafted by the bishops during a weekend retreat - was far from an endorsement of Arroyo, calling for greater accountability and saying her role in an election scandal had undercut the public's trust.
Underscoring the sensitivity and complexity of the issue, the bishops said there was no clear solution and Arroyo must decide if the damage from the crisis is fatal to her leadership. However, they said on Sunday her resignation would not end the political divisions that it has laid bare.
"We ask the president to discern deeply to what extent she might have contributed to the erosion of effective governance and whether the erosion is so severe that it's irreversible," the bishops' statement said.
"She has to make the necessary decision for the sake of the country."
The bishops shunned violence or a forced change of leadership, called for establishment of an independent "truth commission" to probe allegations that Arroyo rigged last year's election, and suggested she could face impeachment proceedings.
"We ask the president to discern deeply to what extent she might have contributed to the erosion of effective governance and whether the erosion is so severe that it's irreversible"
Roman Catholic bishops' statement
"We recognise that non-violent appeals for her resignation, the demand for a truth commission and the filing of an impeachment case are not against the Gospel," the statement said.
"Hence, we also appeal to the people, especially their representatives and leaders, to discern their decisions not in terms of political loyalties but in the light of the Gospel values of truth, justice and the common good."