OAKLAND -- Alex Rodriguez continues to move closer to becoming the seventh player in Major League history to reach the 600-home run plateau, having belted Nos. 596 and 597 on Tuesday off the Athletics' Trevor Cahill in a 6-1 Yankees win.

Rodriguez's first multihomer game of the season included a third-inning grand slam and a sixth-inning solo blast. A-Rod said it made it a little easier to do it at Oakland-Alameda County Coliseum, where the scoreboards aren't tracking his chase to history.

"At home, everywhere I go people are always asking about it," Rodriguez said. "It's hard to ignore. Like I said last week, I'm looking at 600 like first base. You want to run right through it and use it as a springboard for more to come."

Rodriguez has now hit six home runs in his last 13 games, dating back to June 22, a very encouraging sign after the slugger was slowed earlier last month by a groin issue that limited his ability to drive with his hips.

"There have been no setbacks," Rodriguez said. "Every day has been an improvement. That's what I was looking for."

Yankees manager Joe Girardi said that he was pleased that not only is Rodriguez hitting homers at an increased pace, but they have been meaningful shots that have given his team a lead.

"It's wonderful to see," Girardi said. "We know how dangerous of a hitter he is, and even without hitting home runs, he was driving in runs. But when you hit home runs, they can come in bunches."

Rodriguez stepped to the plate against Cahill with the game tied at 1 in the third inning and turned on an 89-mph, 3-1 four-seam fastball, rocketing it to left-center field into the seating pavilion, past the 362-foot sign.

"I just went out there and tried to attack him," Cahill said. "The first time, I threw a four-seamer -- the only one I threw all day.

"My biggest thing, I didn't want to walk in a run right there. I just tried to throw strikes. I wanted to go after him. I wanted to prove I could get him out, but he beat me there."

It was Rodriguez's 21st career grand slam, pulling him even with Manny Ramirez for the second-most in Major League history. Lou Gehrig holds the all-time record with 23.

Rodriguez went deep again against Cahill in the sixth inning, sending a 3-2, 78-mph changeup flying over the center-field wall for his 14th homer of the year, a solo shot that increased New York's advantage to five runs.

Now just three away from his 600th homer, Rodriguez most immediately trails Sammy Sosa (609) on the all-time homers list.

The Yankees have one more game in Oakland and four coming up in Seattle, where Rodriguez's career began, but he said there would be no poetic factor to hitting No. 600 against the Mariners.

"My time in Seattle was terrific and I really enjoyed my time over there, but again, I'm focused on being productive and helping the team win," Rodriguez said.

Actually, if Rodriguez got to pick and choose the date of that milestone, his preference might be to hit No. 600 in the Bronx, where he also belted his 500th shot at the old Yankee Stadium in August 2007.

"Walking the streets of New York, a lot of people are cheering me on," Rodriguez said. "It feels good."