A strike by members of the National Education Health and Allied Workers Union and the Public Servants Association at the SA Revenue Service entered its second day on Friday.
Friday is also the date on which all outstanding tax is due, SARS tweeted.
The unions downed tools on Thursday, as no wage agreement could be reached. SARS indicated that about 33 branches were closed on the first day of the strike.
Negotiations started as far back as November 2018. The parties have engaged over salary increases, as well as improvements in working conditions and benefits.
The Labour Court of South Africa in Johannesburg on Thursday also granted an application by SARS and barred workers represented by the two unions from picketing at all but two SARS branches.
SARS had approached the Commission for Conciliation Mediation and Arbitration (CCMA) to assemble an advisory panel which Nehawu could then approach to make their case.
SARS said in a statement on Friday afternoon that its customs operations at ports of entry, especially borders, have been without major interruptions.
"All customs border posts are operational with the contingencies that have been put in place. Customs has received great support from law enforcement agencies across all border posts, especially from the SA Police Service, and this resulted in minimal impact on them," said SARS.
"SARS assessed media reports, which highlighted a number of trucks piling up at a land border, which could have been attributed to normal traffic and not the strike, as trucks wait for clearance before proceeding."
SARS said it has advised neighbouring countries of the impending strike a few days ago, so that they are not caught by surprise. According to SARS there has been no impact on them.
According to SARS there were isolated attempts to intimidate staff members and to disrupt the flow of traffic at border posts, but the situation was swiftly dealt with by the SAPS.
Fin24 reported earlier that, so far, three offers have been rejected by the unions. This includes the initial 7% increase offered by SARS, as well as a differentiated model. The differentiated model would see top-performing SARS employees who are paid at the lower end receive a 9.2% increase.
No employee would receive an increase of less than 5.2% in this model, according to SARS.
A third proposal, put together by the CCMA, is a multi-year agreement, in which SARS would provide an 8% increase effective from April 1, and would include a consumer inflation plus 1% increase in years 2 and 3 of the agreement, along with other benefits.
Nehawu said it would be open to the 8% increment offer if it were not linked to a multi-term agreement.
SARS encouraged tax payers affected by the closure of branches to use its website to handle their tax affairs while the strike continues.
The latest tweet by SARS indicated that a few more branches had closed by Friday afternoon compared to earlier Friday morning: