Pakistan has carried out raids on a charity believed to be linked to Lashkar, but called on India to provide further evidence.
After visiting New Delhi, Brown travelled to Islamabad, where he was expected to meet Asif Ali Zardari, the country's president.
Brown named Laskhar, also known as LeT, as responsible for the Mumbai attacks, backing India's accusations.
"We know that the group responsible is LeT and they have a great deal to answer for," he said.
"I hope to convey some of the views of the Indian prime minister to the president of Pakistan when I meet him."
Al Jazeera's Kamal Hyder said Brown's statements were "not likely to go down well in Islamabad".
"What Islamabad wants at a time like this, is for other friendly countries to try and help ease the situation," the correspondent said.
Brown said he wanted to come to India to convey his condolences to "the prime minister and the whole of the Indian people at the terrible terrorist outrage in Mumbai that has stunned the whole world".
Brown's arrival in India followed an unannounced visit to Afghanistan where he met British soldiers and hinted that Britain would provide more troops.
The tensions were evident as Islamabad said on Saturday that Indian aircraft violated its airspace - crossing into Pakistan-controlled Kashmir and over the eastern city of Lahore - before being chased back over the border.
India's air force has told Islamabad the incursion was "inadvertent", Sherry Rehman, Pakistan's information minister, said.
India denied any such occurrence.
"The Indian Air Force denies any such violation of airspace," Wing Commander Mahesh Upasani, an Indian air force commander, said, describing Pakistani accusations as an attempt to divert "the attention of the people towards something which has not happened".