On the first full day of his five-day visit, he called for politicians to show commitment to the "common good".
But President Benigno Aquino responded that many Catholic clergy had been silent about the abuses conducted under former President Gloria Arroyo.
And he said some clergymen were now too quick to criticise him.
"In contrast to their previous silence, some members of the clergy now seem to think that the way to be true to the faith means finding something to criticise," he said.
"Even to the extent that one prelate admonished me to do something about my hair, as if it were a mortal sin."
The pontiff arrived in the majority Catholic country on Thursday and is due to travel to the typhoon-hit city of Tacloban on Saturday.
The centre-piece of his visit is an open-air Mass in Manila on Sunday, which is expected to attract millions.
The Pope is on a six-day tour of Asia. Earlier in the week he visited Sri Lanka.
Speaking at a welcome ceremony in the presidential palace, Pope Francis called for leaders "to reject every form of corruption, which diverts resources from the poor".
He said it was a Christian duty to "break the bonds of injustice and oppression which give rise to glaring, and indeed scandalous, social inequalities".
The Philippines, like many countries in Asia, has corruption issues.
Corruption activist group Transparency International put the Philippines at 85 in its latest Corruption Perceptions Index, level with India, Sri Lanka and Thailand.
Under Mr Aquino, the Philippines' record has slowly improved.
Mr Aquino suggested the Church had not done enough to fight corruption under Mrs Arroyo, who is facing charges of plundering state funds and election fixing.
"There was a true test of faith when many members of the Church, once advocates for the poor, the marginalised, and the helpless, suddenly became silent in the face of the previous administration's abuses, which we are still trying to rectify to this very day," Mr Aquino said.
Pope Francis' Philippines schedule
Dancing inmates and Jeepney Popemobile
The BBC's Caroline Wyatt in Manila says there was an atmosphere of celebration on the streets of Manila when the Pope arrived.
Roads in the city centre were shut off, and big screens erected to show the Mass at the Cathedral.
National holidays have been declared in the capital for the duration of the Pope's visit.
Security is very tight, with tens of thousands of soldiers and police deployed, after failed attempts to kill two previous popes in the Philippines.
Pope Francis has urged Philippine leaders to end "scandalous social inequalities" and corruption during a welcome ceremony in Manila.