"We both seek a more secure world for our citizens. We should intensify our defence and law enforcement co-operation to that end," Clinton wrote, in reference to India.
"And we should encourage Pakistan as that nation confronts the challenge of violent extremism."
Clinton's visit to India is aimed at bolstering ties with New Delhi on trade, climate change policy, and arms control.
She is also expected to pay tribute to the 166 people who were killed in an assault on Mumbai in November.
Clinton is set to hold talks with Manmohan Singh, India's prime minister, in New Delhi on Sunday.
Tensions remain
Clinton's apparent effort to smooth ties between India and Pakistan comes amid continued tension between New Delhi and Islamabad.
Although Singh and Yusuf Raza Gilani, his Pakistani counterpart, agreed on Thursday to jointly fight terrorism, Singh has said that formal peace talks with Pakistan are still on hold.
India wants Pakistan to punish those responsible for the Mumbai attacks and stop armed groups from using its territory to carry out attacks in India before the peace talks, known as the composite dialogue, can resume.
"It only strengthens our stand that we wouldn't like Pakistan to wait for the resumption of the composite dialogue ... but take action against terrorist elements regardless of these processes that may lead to resumption," Singh told parliament on Friday.
Washington is aiming to improve relations between India and Pakistan so that it can keep Pakistan's army focused on fighting Taliban fighters based along its western border with Afghanistan.
But India was highly critical when a Pakistani court freed Hafiz Mohammad Saeed, the founder of Lashkar-e-Taiba (LeT), who is wanted for suspected involvement in the Mumbai assaults.
India has arrest warrants against 21 other Pakistanis over the attacks.