Novak Djokovic’s partnership with Andre Agassi has come under serious early pressure in the first week of the French Open. It might not see out the summer.

The defending champion remains on track for a semi-final against the tournament’s perennial prince, Rafael Nadal, but there are cracks showing in his fledgling coaching relationship with Agassi, who missed the first hour of his gruelling five-set struggle against the tough Argentinian Diego Schwartzman in the third round because of commitments with French television.

Asked what he thought of Agassi arriving in his box at 3-4 in the second set, Djokovic said: “He was not supposed to be here today, because we finished yesterday with our in-person collaboration here in Paris. He had many different things that he was supposed to do. He’s doing that. He managed to reschedule certain things and show up today, which was not planned. I appreciate that.”

Further asked about Agassi’s earlier statement on Eurosport that he was doing the gig for nothing, Djokovic said: “I’m not going to get into that but everything he said is completely true, so it’s completely his decision. I hope that’s going to stay for a long time that we can create something that is going to go long term. We don’t have anything set in stone. We had a great chat after the match. He’s going to try his best to be in the biggest tournaments with me as much as his family time allows and all the commitments that he has.”

Agassi had already told Djokovic that, after he is done here, he must leave to fulfil earlier commitments, possibly after his next match, against Albert Ramos-Viñolas, who beat Lucas Pouille, 6-2, 3-6, 5-7, 6-2, 6-1 in fading light.

In an interview on Eurosport with Boris Becker, who guided the Serb to six of his 12 major victories before they ended their three-year relationship last December, Agassi revealed he was working at Roland Garros “on my own time, on my own dime, my own money”. No doubt his link with the tournament sponsors, Longines, will ease the financial burden of spending a week in Paris.

“I don’t want anything, I don’t need anything, I want to help him,” he said. Djokovic needed all the help he could get quelling Schwartzman’s determined challenge over three hours and 19 minutes.

There is something awry with the world No2’s tennis again, after a few encouraging weeks lately. There were some rough moments, none more awkward than at break point on his own serve, 4-0 up in the fourth. Djokovic received a time warning, then a code violation. He was not putting a lot of love the umpire’s way during a 5-7, 6-3, 3-6, 6-1, 6-1 win.

Agassi revealed a little of his tennis philosophy and how he might persuade Djokovic to switch from lights-out attack to more thoughtful ways of breaking opponents down.

“For me it’s simple. His game is built on controlling the baseline and executing to big targets. He’s not a guy that plays precisely to the lines. Occasionally if he’s on the defence he surprises you with this. He’s a guy that throws body blow after body blow after body blow and he’s just never thought a lot about the other side of the court. So I think there’s ways he can take his game at 30 years old – and older because hopefully he’s going to still want to play for a while – and he can start to make it easier for himself by knowing what to do across the net.”

He sounded equivocal about working with Djokovic at Wimbledon. “If he wants me there, I will come and figure it out. It is a lot of responsibility. Whatever is practical and achievable, 100% I will make the effort. I committed to him that, as long as he feels like I can help him, I will. Does he really need me somewhere in particular, does he need me in a week off, does he need me in a grand slam? We will figure this out as we go. A 100% I am committed to seeing him achieve what his dream is.”

Nadal spent probably as much time arranging his courtside water bottles as he did constructing 27 clear winners among 82 points to beat Nikoloz Basilashvili 6-0, 6-1, 6-0. The Georgian, who last year lost to Kyle Edmund in the first round, went downhill faster than Franz Klammer.

At the end patrons were treated to the rare spectacle of Nadal abandoning his hair-tugging, ball-bouncing rituals as he served out the match like a man with his pants on fire just as the first of the intermittent rain dumped on Court Philippe Chatrier. “Today was one of the best matches I have ever played, without a doubt,” Nadal said later.

If he and Djokovic do clash for a place in the final, the odds would be with the Spaniard, who has won 20 of 21 matches on clay this season. This was his 100th best-of-five match on his favourite surface. Only Robin Soderling here in 2009 and Djokovic two years ago have prevailed against him, a phenomenal record.

Before the quarter-finals Nadal will celebrate his 31st birthday on Saturday then, if all goes well, follow it with a win over his compatriot, Roberto Bautista Agut, who beat Jiri Vesely 6-3, 6-4, 6-3.