Martin's Swansea were beaten for the fifth time in their last six Championship games at Millwall on Tuesday
Head coach Russell Martin says he has been told he is "not going anywhere" by Swansea City co-owner Steve Kaplan despite his team's slump in results.
Kaplan made a rare appearance at a Swansea game as they were beaten 2-1 at Millwall on Tuesday.
Swansea have won three of their last 21 league games, but Martin says Kaplan "offered his support" during a pre-match chat.
"Steve is good guy. We speak regularly," Martin said.
"He was here for a couple of hours today which was great. We spoke a lot about the summer, about tonight, about recent events. It was a good, honest conversation.
"As I spoke about at the end of January, Steve has been great since I have been at the club.
"The final say is not with Steve. Obviously he's heavily involved. He has been great since we have been here."
American businessmen Kaplan and Jason Levien led a consortium which took charge at Swansea in 2016.
It is understood Levien made the final call on transfers during Swansea's miserable January window, when they failed to sign a player.
Since then, Swansea have won one and lost seven of their nine Championship games.
Martin's team produced an impressive performance at Millwall, but the defensive lapses which have been an issue for much of the season once again cost them dear.
Having been as high as fourth in the table last October, Swansea now lie 17th, eight points clear of the relegation zone.
When asked whether Kaplan had given him a vote of confidence during their conversation, Martin said: "He has told me I am not going anywhere, so I trust him with that.
"I hate that term [vote of confidence], but he has offered nothing but support and encouragement for the long-term plan. He just wants us to grow and get better."
Swansea host Bristol City in their final game prior to the international break on Sunday, before returning to action with the south Wales derby at Cardiff City on Saturday, 1 April.
"We need to win a couple of games to relax everyone and make sure we have enough momentum going into next season for sure," Martin added.
"Over the last three games, the performances have been building back up again to some level we want them at.
"Tonight [at Millwall] is the best we have played in a long, long time. I hope it will keep building confidence."