"I visited the National Police Memorial this morning and paid tributes to our martyrs of the central and state police forces, who have sacrificed their lives in the line of duty," he tweeted after visiting the memorial located in the capital's Chanakyapuri area.
The home minister said he was overwhelmed after visiting the memorial which was erected as a mark of respect to over 34,000 policemen who sacrificed their lives protecting the nation.
"I salute their valour and courage. A grateful nation is indebted to them for their supreme sacrifice," he said.
Union Home Secretary Rajiv Gauba and Director of the Intelligence Bureau Rajiv Jain accompanied Shah.
Shah took charge as Union Home Minister on the second day after he was sworn-in following a landslide victory of the saffron party-led NDA. Two Ministers of State for Home (MoS Home) - G K Reddy and Nityananda Rai - also took charge Saturday.
Shah got to work soon after assuming office. On Saturday, he sought briefing about security situation in Jammu and Kashmir, which is currently under the President's rule, from Governor Satya Pal Malik.
A home ministry official said Shah is expected to prioritise the NDA government's policy of zero tolerance towards terrorism and checking illegal immigration.
During the 15-minute meeting, the Governor apprised the home minister about the preparation for the Amarnath Yatra.
Discussions were also held between the two on the law and order situation in the Kashmir Valley and the border areas besides various development issues.
"I have discussed security matters and development issues with the Home Minister," Malik told reporters after the meeting.
The Governor, however, said that the issue related to holding assembly elections in the state was not discussed as the matter was under the purview of the Election Commission of India.
Jammu and Kashmir is under the central rule since June 2018 and the assembly election is expected to be held later this year.