Решено, это можно сделать с помощью RestSharp:
RestClient client;
public API()
{
client = new RestClient("https://127.0.0.1:40/");
ServicePointManager.Expect100Continue = true;
ServicePointManager.DefaultConnectionLimit = 9999;
ServicePointManager.SecurityProtocol = SecurityProtocolType.Tls | SecurityProtocolType.Tls11 | SecurityProtocolType.Tls12 | SecurityProtocolType.Ssl3;
ServicePointManager.ServerCertificateValidationCallback += (sender, certificate, chain, sslPolicyErrors) => true;
var certFile = "lxd.pfx";
X509Certificate2 cert = new X509Certificate2(certFile, "(password)");
client.ClientCertificates = new X509CertificateCollection() { cert };
client.Proxy = new WebProxy();
}
public void Test()
{
var restrequest = new RestRequest("1.0/networks", Method.GET);
IRestResponse response = client.Execute(restrequest);
Logging.Log(response.Content, "API", LogLevel.INFO);
}