Bangladesh spin bowling coach Mushtaq Ahmed said he believed his side could still snatch their first-ever Test win against South Africa at the Sher-e-Bangla National Stadium in Mirpur.

Mehedi Hasan Miraz and Jaker Ali struck half-centuries as Bangladesh staged a fightback with an 81-run lead before bad light brought an early finish to day three of the first Test on Wednesday.

Miraz and debutant Jaker added 138 runs for the seventh wicket to save Bangladesh from an innings defeat after they resumed at 101-3, chasing down South Africa's 202-run first-innings lead.

Jaker was eventually trapped lbw by left-arm spinner Keshav Maharaj for 58.

The hosts were 283-7 in Mirpur when the umpires called stumps about an hour before the scheduled finish, with Miraz unbeaten on 87 and Nayeem Hasan not out on 16.

Former Pakistan spinner Mushtaq appeared in the post-day press conference and exuded confidence over his side's chances of winning the match.

"Why not? You just have to believe that. Every time you talk about belief -- it's about the process and not giving up. When you don't give up, the opposition also respects that you can," he told reporters in response to a question about whether it's possible for his side to win this match.

"From my point of view, we have to believe. The belief has to be there, from any situation. And when you have belief and confidence, you can challenge any team. So we have to bat as long as we can, score consistently, and get whatever lead we can," he added.

South Africa only bowled five overs in the last session, and fewer than 58 overs were played throughout the day after a rain interruption cut the second session short.

In the morning, South African pace bowler Kagiso Rabada took advantage of overcast conditions to take two wickets in three balls during the fifth over.

Mahmudul Hasan Joy departed after making 40 when his attempted drive found a thick edge to first slip, where David Bedingham took the catch.

Rabada's fourth wicket of the innings came two balls later as he sent Mushfiqur Rahim's middle stump cartwheeling out of the ground with a full delivery that nipped back. The right-hander made 33.

Wicketkeeper Liton Das followed for just seven as he edged a sharply turning delivery from Maharaj to wicketkeeper Kyle Verreynne, and the dismissal was confirmed as caught on review after an initial shout for lbw.

South Africa scored 308 in their first innings, powered by Verreynne's second Test century, in reply to Bangladesh's 106 all out on the opening day.