US officials often accuse Pakistan of helping militants, a charge Islamabad vehemently denies, but this marks the first time that the allegation has been attributed to Mr Trump.
"The President has also made clear that we need to see a change in behaviour of those in the region, which includes those who are providing safe haven and support bases for the Taliban, Haqqani Network and others," General McMaster said.
Banned outfits such as the Taliban and Haqqani Network operate and move freely in parts of Pakistan close to the border of Afghanistan. Kabul has repeatedly blamed Islamabad for violence in the country.
"This is Pakistan in particular that we want to really see a change in and a reduction of their support for these groups. This is of course, you know, a very paradoxical situation where Pakistan is taking great losses. They have fought very hard against these groups, but they've done so really only selectively," he said.
According to General McMaster, the US President "does not want to place restrictions on the military that undermine our ability to win battles in combat".
The US media reported earlier this week that in a July 19 meeting at the White House, Mr Trump berated his generals for not winning the war in Afghanistan and allowing the violence to continue for more than 16 years.
Mr Trump also "repeatedly suggested" to his senior military advisers that they should replace General John Nicholson, the commander of US and NATO forces in Afghanistan, with a new General who could win the war.
But General McMaster disagrees with Mr Trump's suggestion. For General Nicholson, General McMaster said: "Of course. I've known him for many years. I can't imagine a more capable commander on any mission."
Mr Trump has authorised the Pentagon to take the lead on military decisions in Afghanistan, although he formed a separate team of experts for a new Afghan policy.