The arrest comes three days after three terrorists including a top Jaish-e-Mohammed (JeM) commander were killed in an encounter with the security forces in Awantipora.
"Lashkar-e-Toiba terrorist Nisar Dar arrested by J&K Police & Security Forces. He had escaped from an encounter in Kullan Ganderbal in which one Pakistani terrorist of proscribed terror outfit was killed. This dreaded terrorist was wanted in many terror crimes," Hussain tweeted.
A UN-proscribed terrorist, Saeed is the main accused in the 2008 Mumbai terror attacks, which killed around 165 people, including foreign citizens. His group, Lashkar-e-Taiba, is also accused of carrying out the 2001 Indian Parliament attack.
Trump's remarks on Saeed's arrest came ahead of the maiden visit of Prime Minister of Pakistan Imran Khan to the US. The meeting would focus on improving bilateral ties between the two countries.
Cases were registered under the Anti-Terrorism Act against five proscribed outfits in Lahore, Gujranwala, and Multan - Dawatul Irshad Trust, Moaz Bin Jabal Trust, Al Anfal Trust, Al Madina Foundation Trust, and Al Hamd Trust.
Around 400 people from India, the Caribbean countries, Bangladesh, Sri Lanka, Israel, Balochistan (part of Pakistan) expressed staged the protest.