"I visited the National Police Memorial and paid tributes to our martyrs of the central and state police forces who have sacrificed their lives in the line of duty. I salute their valour and courage. A grateful nation is indebted to them for their supreme sacrifice," the Minister tweeted.
In another tweet in Hindi, Shah said it was his first public programme after taking charge as the Union Home Minister.
"I paid tribute to over 34,000 personnel from police and security forces who sacrificed their lives. Our country is safe because of the sacrifice of these personnel.
"...I am feeling energetic after visiting here. Also, the feeling to do everything for the country has become more strong."
Shah was accompanied by Union Home Secretary Rajiv Gauba and Intelligence Bureau chief Rajiv Jain among other senior officials.
During his visit, he wrote in the visitors' book and offered flowers in front of the Wall of Valour.
Former Home Minister and now Defence Minister Rajnath Singh on Saturday paid tribute at the memorial before taking charge.
The National Police Memorial commemorates 34,844 police personnel from all the central and state police forces in India who have died in the line of duty since India's Independence in 1947.
( With inputs from IANS )