Peers were warned to be "very, very careful" about making a fresh attempt to resurrect the Leveson inquiry after MPs rejected their proposals for a second time.
Culture Secretary Matt Hancock's warning to the House of Lords came as he made concessions over press regulation, including regular reports on the effectiveness of low-cost arbitration and how personal data is processed for journalism purposes.
Mr Hancock was forced to make amendments to the Data Protection Bill after peers sent it back to the Commons demanding a further investigation into the relationship between the media and police, among other issues.
But the Cabinet minister said the Commons had "plainly and clearly" voted against the initial amendments moved by peers to reopen the Leveson inquiry, as he urged MPs to reject the latest measures.
He said: "I support the convention that if something is in the party of government's manifesto and this House passes it, then the Lords should be very, very careful about sending it back."
Mr Hancock added: "I hope the vote of this House today is respected because we will then have considered this question twice. We have made concessions in order to take on board legitimate concerns, but ultimately this House will have decided its view having considered the question twice."
The Culture Secretary explained the amendments would bolster the powers of the Information Commissioner and ensure its review of good practice and compliance of data protection regulations by journalists occurs every five years.
Further advancing calls for a second inquiry, he said that a "minority of the press" had engaged in the "most abusive and intrusive activity" and needed to be examined.
He said: "I hope members across this House think about our responsibilities to the victims, the promises we made, that this inquiry does have a clear purpose and that only this inquiry can get to the truth about what happened and learn lessons for the future."
Peers will have to consider the amendments made by MPs before the Bill can become law.