She would meet them as part of her presidential poll campaign, A C Kaushik, office secretary of the Punjab Congress Legislature Party (CLP), said on Friday.
The meeting between Ms Kumar and the Congress lawmakers had been convened by Punjab Chief Minister Amarinder Singh, who was also the leader of the Punjab CLP, he added.
At the meeting, Ms Kumar would seek the support of the MLAs and MPs for the July 17 presidential election, said Kaushik.
While the ruling Congress has 77 MLAs in the 117-member Punjab Assembly, the Aam Aadmi Party (AAP) has 20, its ally the Lok Insaaf Party has two and the SAD-BJP coalition has 18 legislators (Shiromani Akali Dal 15, BJP three).
Among the Lok Sabha members from Punjab, four belong to the Congress, three to the SAD, two to the BJP (though the saffron party's MP from Gurdaspur, Vinod Khanna, passed away recently), four to the AAP, of whom, two have been suspended by the party.
In the Rajya Sabha, the SAD and the Congress have three members each, while the BJP has a lone representative from the state in the Upper House of Parliament.
The presidential election is scheduled for July 17 and the counting of votes will be taken up on July 20.
On June 29, the ruling NDA's presidential nominee and former Bihar governor, Ram Nath Kovind, had held a meeting with the SAD-BJP lawmakers from Punjab and Haryana at Panchkula, near Chandigarh.
Follow detailed coverage on Presidential Election 2017 here