Corey Oswalt of the Mets pitches in the first inning...

Corey Oswalt of the Mets pitches in the first inning against the Washington Nationals at Citi Field on Sunday. Credit: Jim McIsaac

Corey Oswalt took the mound Sunday against Washington with no idea of what Mets manager Mickey Callaway had said about him before his fourth major-league start.

While many figured Jason Vargas, who pitched well Saturday in a rehab start with Class A Brooklyn, could return as the Mets’ fifth starter, Callaway left the door open for Oswalt.

“I think we need to evaluate where everybody is at over the All-Star break,” Callaway said before Sunday’s game. “We’ll see how [Oswalt] does and we just have to figure out what’s best for our team.”

The 6-5, 245-pound right hander made his manager look good in only his fifth big-league outing. Oswalt allowed a run, two hits and no walks in five innings. The rookie threw 73 pitches, including 51 strikes.

“I just go out there and do what they might need,” said Oswalt, who is 0-2 with a 5.64 ERA. “Try to keep the ballgame close and help the team win.”

He did his part Sunday. The bullpen did not, allowing five runs in the seventh inning as Oswalt got a no-decision in the Mets’ 6-1 defeat. He was lifted in the fifth for a pinch hitter with Jose Reyes on third base, two outs and the score tied at 1. (The Mets had only two hits at that point.)

“He’s pitched really well, and I think his ability to throw the ball over the plate really helps him out,” Callaway said. “He stays ahead in the count.”

Oswalt has been working on keeping his back leg more upright to help his delivery.

“It’s definitely improved, and Dave [Eiland, the pitching coach] has really helped me get the downward angle on my pitches so I’m not as flat,” Oswalt said. “I’m starting to attack guys.”

Callaway has noticed Oswalt’s improvements.

“We value [throwing strikes] in a pitcher, and he has done a pretty good job of that,” he said. “He’s definitely opened some eyes, and he’s going to make decisions really tough.”

Vargas said he will throw a side session at Yankee Stadium after the All-Star break.

“I’m hoping that everything goes well,” said Vargas, who threw 90 pitches (including 64 strikes) Saturday. “[Then] we go to the next step. I guess we have to see how things line up. I haven’t gotten too concerned with that. I figure that things usually work themselves out.”

Oswalt feels the same way about how the Mets will fill their fifth-starter slot. “I don’t worry about any of that stuff,” he said.

Only Callaway and the Mets’ brass know what that step will be.

“It’s good to know we have options with Vargas now being healthy,” Callaway said. “So we’re going to sit down over the break and try to figure out exactly what is best for our team for the second half.”