The companies still need approval from 20 competition regulators.
Nokia has received approval from the US Department of Justice for its $17.6bn deal to acquire French telecommunications-equipment rival Alcatel-Lucent.
The approval has brought the companies one-step closer to the completion of the acquisition, but it still needs the green signal from 20 competition regulators to go ahead with the takeover.
This will include approval from China and the European Union.
Nokia said: "The parties continue to make good progress with the regulatory approval processes in the remaining relevant jurisdictions, with the parties having already obtained antitrust clearances in Brazil and Serbia.
"Both companies will continue to cooperate with the remaining authorities to close their reviews as quickly as possible."
Nokia is also seeking approval from the Committee on Foreign Investment in the US, the regulatory body which reviews foreign acquisitions of US businesses in order protect national security.
The acquisition is expected to overshadow Ericsson AB and Huawei Technologies in wireless-infrastructure revenue.
The companies are expecting the deal to close next year, with Nokia expecting savings of €900m by 2019.
In 2015, Nokia and Alcatel-Lucent had combined sales of about €26bn last year.