The storm has killed more than 6000 people and displaced four million. US Marines and humanitarian groups have joined in a multimillion-dollar relief effort to deliver aid to survivors and Mr Kerry yesterday visited a distribution centre.
While the US has said it does not intend to open new military or naval bases in the region, Mr Kerry discussed ways the US could help respond quicker during disasters.
His visit to south-east Asia comes as the US strives for a trade deal with 11 countries in the Asia-Pacific region.
A Trans-Pacific Partnership trade pact is the centrepiece of US efforts to refocus attention on the fast-growing region. The Philippines has expressed interest in joining the pact and Mr Kerry said a delegation from Manila would visit Washington in January for talks.
Maritime security also featured in Mr Kerry's talks with President Benigno Aquino, as it did on his stop in Vietnam earlier this week.
The Philippines has a £1 billion spending plan to upgrade its military capabilities, particularly surveillance and monitoring systems on its maritime borders in the South China Sea.
Mr Kerry said the US would give £25m to help stiffen maritime security.