The Democratic Alliance says only Parliament can recall President Jacob Zuma, and that the ANC's resolution is nothing more than an internal resolution.
"It has no effect on Jacob Zuma's current status as President of the Republic, and can be simply ignored by Zuma," DA leader Mmusi Maimane said on Tuesday.
"Unless he tenders his resignation, this recall is not worth the paper it is printed on."
ANC secretary general Ace Magashule announced on Tuesday that the party's national executive committee had agreed to recall Zuma following a marathon 13-hour meeting on Monday.
No deadline has been given to Zuma. However, Magashule said he "expects" an announcement from Zuma on Wednesday.
Maimane said that Zuma remains president, and in power until he resigns or is removed in Parliament.
"And as long as this is the case, our country suffers.
"The only way to remove Jacob Zuma as President of our country is for Parliament to do so through a motion of no confidence. It is Parliament that elects and removes a President, not the ANC."
Maimane again called for the EFF's motion of no confidence, provisionally scheduled for February 22, to be urgently brought forward to this week, in order for Parliament to remove Zuma.
"Following that, the National Assembly must dissolve Parliament in terms of Section 50 of the Constitution," he argued.
"Anyone who wants to be the next President of this country must have the mandate of the people, and this can only be established through an early election."
The people must elect the new South African President, not a few connected cadres within the ANC, he concluded.
ANC must now remove 'parasitic networks'
The South African Communist Party, vocal opponents of Zuma over the past 12 months, has welcomed the ANC's decision to recall Zuma as president.
"The immediate tasks moving forward include dismantling the parasitic networks surrounding our state and movement and deal decisively with corporate state capture and other forms of corruption," spokesperson Alex Mashilo said.
"This must be guided by an intensified effort to selflessly serve the people exceptionally and solve their problems with loyalty."
Priority had to be given to radically reducing and eliminating high levels of class, race and gender inequalities.
Mashilo said the SACP hoped the decision would lead to a deeper unity and reconfiguration within the "ANC-headed" alliance, in order to win the 2019 elections.
The UDM also welcomed the decision to recall Zuma.
"It has taken far too long for this to happen, once it became patently clear (years ago) that he was not fit to hold the highest office in the country," UDM leader Bantu Holomisa said in a statement.
'ANC must own the mess'
He said the ANC only reached this decision "because of the continued, consistent pressure exerted by opposition parties; civil society; and the media, who played a critical role in exposing institutionalised corruption such as #GuptaLeaks".
"The ANC's much vaunted self-correcting nature is a damp squib. South Africans, especially eligible voters, have realised that the ANC has lost its moral high-ground and had relinquished its status as South Africa's liberation movement.
"If it wants to be taken seriously, the ANC - which has been protecting Mr Zuma, at all cost - must own up to this mess and immediately charge Mr Zuma and his fellow gangsters. In the end him and his colleagues your deployees!"
He said the UDM was positive about the future, but recognised that it would take South Africa years to recover from the damage caused by the Zuma administration.
"However, only half the battle has been won at this time. All patriotic South Africans, opposition parties, civil society, and the media should not now rest and lower their guards. We must ensure that the culprits face the full might of the law and that the billions of stolen Rands be returned to the last cent!"
The Economic Freedom Fighters, meanwhile, gave National Assembly Speaker Baleka Mbete until 13:00 on Tuesday to respond to a request to move their motion of no confidence in Zuma forward to this week.
The party said it would proceed with a court challenge if she failed to meet the deadline, or chose not to accede to the request. The EFF has yet to comment on both the issue of Zuma's recall and the motion of no confidence.