Vadra is the son-in-law of Congress president Sonia Gandhi.
Asked about the Change of Land Use (CLU) related decisions of the previous Bhupinder Singh Hooda government and investigation concerning Vadra's land deals, Khattar said: "Law will take its own course on all such complaints."
"My government would not act with the spirit of vendetta. The priority of the state government is to implement its agenda aimed at the welfare of people of the state."
Khattar's comments are being seen as a softening of stand of the new BJP government on the land scams during the Hooda regime.
The land scams were a major issue raised by the Bharatiya Janata Party during the poll campaign.
Two senior ministers, Ram Bilas Sharma, who is also the Haryana BJP president, and Anil Vij, Sunday said a judicial probe would be ordered into the land scams.
"We are certainly opening those cases. A high court judge will inquire into these," said Sharma, the seniormost minister in the Khattar government.
Vadra has been accused of making millions of rupees in land deals during the Hooda government between March 2005 and October 2014.
Vij said: "Land is the biggest scam that has taken place in Haryana."
"Over 70,000 acres of land was acquired (by the Hooda government) from innocent farmers and allotted to people after making huge profit. We will get every inch of this land scam probed. Anyone found guilty, whether any official, Robert Vadra or Bhupinder Singh Hooda, we will not spare anyone," he said.