House Republicans on Monday made a fresh deficit-reduction proposal to the White House that calls for $800 billion in increased tax revenue, half of what President Barack Obama has proposed.

The GOP offer was immediately rejected by the White House, but it provides the most detailed statement to date of what Republicans are willing to concede for now. It comes days after the White House put forward its opening bid in the high-stakes deficit talks. With both sides now having made preliminary offers, the parameters for future...