Turkey and the United States have sparred publicly for months over Ankara's order for the S-400s, which are not compatible with NATO's systems.
"Turkey has already bought S-400 defence systems. It is a done deal. I hope these systems will be delivered to our country next month," Erdogan said.
The purchase has raised eyebrows among Turkey's NATO allies and provoked anger in Washington, which expected Ankara to opt for the American Patriot air defence system instead.
The Pentagon announced on Friday that if Turkey did not give up on the S-400 system by July 3, Ankara would be blocked from purchasing F-35 fighter jets and Turkish pilots currently training in the US would be expelled.
Turkey plans to buy 100 F-35s from the US.
On Monday, US officials announced that Washington had halted the training of Turkish pilots on F-35 fighters at an airbase in the US state of Arizona.
US acting Secretary of Defense Patrick Shanahan said last week he had sent a letter to his Turkish counterpart Hulusi Akar informing him of Washington's decision to pull Turkey out of the F-35 programme.
'Spirit of the NATO alliance'
Turkey has criticised the letter from Washington and said it did not live up to the spirit of the NATO alliance. It is working on a response to be sent in the coming days, according to the Turkish defence minister.
The US says Turkey's acquisition of the Russian system poses a threat to Lockheed Martin Corp's F-35 stealth fighters and has warned of potential US sanctions if Ankara presses on with the deal.
Erdogan vowed to seek answers on his country's "exclusion from F-35 project for reasons that have no rational or legitimate basis", adding that Turkey was not only a customer but also a programme partner of the F-35 project.
Speaking at a meeting of his AK Party members, Erdogan said: "We will call to account in every platform Turkey being excluded from the F-35 programme for reasons without rationale or legitimacy."
"We have so far paid $1.250bn," he said.
Shanahan said on Friday the US offer for the Patriots was "very competitive" but Erdogan said Russia offered a better deal including reasonable pricing and a joint-production promise.
"This is not an attack system but a defence system. Won't we take necessary measures to defend our country?" he said.
"Did we ask for such a defence system from America? Yes, we did. Did they deliver? No, they didn't," he said.
Turkey has repeatedly proposed a joint-working group to assess the impact of the S-400 deal, but Washington has not yet taken up the suggestion.
Erdogan also said he wanted to talk about the issue on the phone with the US before he meets President Donald Trump in Osaka, Japan, at the end of this month.
The Turkish leader said he "would like to discuss this issue by telephone and reverse it from the current situation back to where we started".
Russia said on Tuesday it planned to deliver its S-400s to Turkey in July.