A subdued President Reagan welcomed House approval of the $98.3 billion tax bill last night as a "milestone" in his economic recovery efforts, but immediately turned his attention to healing wounds left in his party by the bruising fight he waged for yesterday's narrow victory.

Quiet handshakes were exchanged in a tiny room near the Oval Office as the president watched the final two minutes of voting in the House on closed-circuit television with his top aides. But the mood was in marked contrast to the open jubilation that has followed Reagan's earlier victories in Congress.

A few minutes later, in a brief appearance before reporters in the Oval Office, the president declared that yesterday's vote "does not mark the end of the crusade to get our country's economy moving again, but it is an important milestone."

Reagan, now on the threshold of the fall congressional campaigns that will focus in large part on his handling of the economy, moved after yesterday's victory to soothe conservative Republicans who had opposed the tax bill and to promise the American people that better days lie ahead.

"Let's leave our differences behind us and all of us get on with the nation's business," Reagan said. "To those who voted against us, honorable men and women can honestly disagree. They can also leave their disagreements behind them, and work together once the issue is settled by free and open voting."

Asked whether he thought the three-year tax bill would be a liability in the fall campaigns when consumers feel the brunt of new taxes on cigarettes and telephone use, among other things, the president said: "No, I don't think it's going to hurt anyone in November, frankly."

And he made it a point to reaffirm his commitment to tax cuts in the wake of a crescendo of complaints from his old conservative allies in recent weeks that he had abandoned faith in supply-side economic theory.

"To even have referred to this as a tax increase I think was wrong," Reagan told reporters, "because it was an adjustment of the tax cut passed last year and which still continues on into the coming years."

"I think there was a perception on the part of some and an alarm that this represented some kind of change in philosophy -- it does not. I still believe in the combination of incentive tax cuts that will increase productivity in this country and . . . reductions in spending."

The themes of Reagan's fall campaign will be struck in appearances next week and on Labor Day, and the president expressed confidence yesterday that Republicans will be meeting the voters in an improved economic climate after months of recession and rising joblessness.

"I think what they are going to see and what they are going to be thinking about is that the economy is going to continue to improve. I think that failure to pass this would have been a setback to improvement in the economy . . . all the indices we have now are supportive of the idea that things are getting better."

The $98.3 billion tax increase that cleared the House yesterday will take back about a quarter of the three-year tax cut Reagan won from Congress in 1981, and the president said yesterday that there is still plenty of stimulus remaining in the personal income tax cuts that were left intact.

"And the truth of the matter is, even with this passed, the tax cut over the next three years will amount to $335 billion for the people next year -- they will double the gain they have already made in their personal fortunes because of the tax cut," Reagan said.

It was a bittersweet day for Reagan as he felt the personal loss of Dr. Loyal Davis, stepfather of Nancy Reagan, who died in Scottsdale, Ariz. of congestive heart failure. The president, who had postponed his California vacation to pressure Congress for the tax bill, plans to leave the White House today for a memorial service in Phoenix for Dr. Davis.

In a two-week lobbying drive in which he employed presidential perks, such as a Sunday lunch at Camp David, and his own forceful personal persuasion, the president talked to more than 150 congressmen in an effort to overcome a conservative revolt against the tax bill.

But Reagan did not watch the long debate on closed-circuit television as it was played out in other White House offices yesterday. Instead, he gathered at the last minute, to watch the final votes being cast, with White House officials and Defense Secretary Caspar W. Weinberger and Secretary of State George P. Shultz, according to Deputy White House press secretary Larry Speakes.

Asked whether he was getting nervous with so many Hill victories, Reagan quipped: "Don't talk like that. As an old sports announcer, I have to tell you that when a no-hitter is being pitched, you never mention it during the game. You'll jinx the pitcher."