He angered Pakistan when he suggested it was promoting the export of terror.
At the weekend, a Pakistani intelligence chief cancelled a UK trip, and President Asif Ali Zardari has been under pressure to cancel a visit to Britain on Tuesday.
A spokeswoman for Mr Cameron said he "stands by his comments".
During his trip to Pakistan's regional rival India last week, Mr Cameron said: "We should be very, very clear with Pakistan that we want to see a strong, stable and democratic Pakistan.
"We cannot tolerate in any sense the idea that this country is allowed to look both ways and is able, in any way, to promote the export of terror, whether to India or whether to Afghanistan or anywhere else in the world."'Misperception'
In the Pakistani capital Islamabad on Monday morning, Britain's high commissioner Adam Thomson answered a summons from Foreign Minister Shah Mehmood Qureshi.
The UK Foreign Office said in a statement afterwards: "The high commissioner and Foreign Minister Qureshi discussed a broad range of bilateral issues, including President Zardari's upcoming visit to the UK."
The Pakistani leader has a five-day UK visit planned, including potentially fraught talks with Mr Cameron on Friday.
After holding talks in Paris on Monday with French President Nicolas Sarkozy, Mr Zardari said France saw Pakistan as a "reliable partner in the world".
Speaking at the Elysee Palace, he said President Sarkozy would visit Pakistan later this year.
Pakistani Information Minister Qamar Zaman Kaira has said Mr Zardari will seek to correct Mr Cameron's "misperception" during his UK visit.
Mr Cameron's spokeswoman said he had acknowledged Pakistan was taking action against extremism and insisted his comments last week had referred to elements within Pakistan supporting terrorism, not to the Pakistani government.
Asked about the burning of an effigy of the prime minister in Karachi, she said: "People have a right to protest."
Mr Kaira told the BBC the Pakistani government had reacted properly, and that Pakistan had been "hurt" by the comments as the country was a victim of terror as well as a key fighter against it.
"But the president and our government feels we should interact with the British government and we should explain and discuss, and put the proper and right perspective in front of the British government and British prime minister so that any misperception or misconception should be over," he said.Classified files
The diplomatic fallout from the comments led Pakistan's spy agency, Inter Services Intelligence (ISI), on Saturday to cancel a visit to Britain to discuss counter-terrorism with UK security services.
Mr Cameron's remarks followed the leaking of US documents on the Wikileaks website in which the ISI was accused of secretly helping the Afghan insurgency.
According to the classified files, Pakistani agents and Taliban met to organise the fight against US soldiers in Afghanistan and plotted to assassinate Afghan leaders.
But Islamabad says it is as much a victim of terrorism as any other country - home-grown Taliban and al-Qaeda-linked bombers have killed more than 3,500 people in a three-year campaign.
Pakistan's military won plaudits from the international community last year when it launched major operations against the militants in South Waziristan and the Swat valley on the Afghan border.