diff --git a/lib/net/http/generic_request.rb b/lib/net/http/generic_request.rb
index c92004e..e19c63a 100644
--- a/lib/net/http/generic_request.rb
+++ b/lib/net/http/generic_request.rb
@@ -19,16 +19,17 @@ def initialize(m, reqbody, resbody, uri_or_path, initheader = nil) # :nodoc:
 
     if URI === uri_or_path then
       raise ArgumentError, "not an HTTP URI" unless URI::HTTP === uri_or_path
-      hostname = uri_or_path.hostname
+      hostname = uri_or_path.host
       raise ArgumentError, "no host component for URI" unless (hostname && hostname.length > 0)
       @uri = uri_or_path.dup
-      host = @uri.hostname.dup
-      host << ":" << @uri.port.to_s if @uri.port != @uri.default_port
+      @host = @uri.host.dup
+      @port = @uri.port == @uri.default_port ? nil :  @uri.port
       @path = uri_or_path.request_uri
       raise ArgumentError, "no HTTP request path given" unless @path
     else
       @uri = nil
-      host = nil
+      @host = nil
+      @port = nil
       raise ArgumentError, "no HTTP request path given" unless uri_or_path
       raise ArgumentError, "HTTP request path is empty" if uri_or_path.empty?
       @path = uri_or_path.dup
@@ -51,7 +52,7 @@ def initialize(m, reqbody, resbody, uri_or_path, initheader = nil) # :nodoc:
     initialize_http_header initheader
     self['Accept'] ||= '*/*'
     self['User-Agent'] ||= 'Ruby'
-    self['Host'] ||= host if host
+    self['Host'] ||= @port ? "#{@host}:#{@port}" : @host if @host
     @body = nil
     @body_stream = nil
     @body_data = nil
@@ -245,7 +246,7 @@ def update_uri(addr, port, ssl) # :nodoc: internal use only
     end
 
     if host = self['host']
-      host.sub!(/:.*/m, '')
+      host = URI.parse("#{scheme}://#{host}").host # Remove a port component from the existing Host header
     elsif host = @uri.host
     else
      host = addr
diff --git a/test/net/http/test_http_request.rb b/test/net/http/test_http_request.rb
index 7fd82b0..9f5cf4f 100644
--- a/test/net/http/test_http_request.rb
+++ b/test/net/http/test_http_request.rb
@@ -74,6 +74,18 @@ def test_initialize_GET_uri
     assert_equal "/foo", req.path
     assert_equal "example.com", req['Host']
 
+    req = Net::HTTP::Get.new(URI("https://203.0.113.1/foo"))
+    assert_equal "/foo", req.path
+    assert_equal "203.0.113.1", req['Host']
+
+    req = Net::HTTP::Get.new(URI("https://203.0.113.1:8000/foo"))
+    assert_equal "/foo", req.path
+    assert_equal "203.0.113.1:8000", req['Host']
+
+    req = Net::HTTP::Get.new(URI("https://[2001:db8::1]:8000/foo"))
+    assert_equal "/foo", req.path
+    assert_equal "[2001:db8::1]:8000", req['Host']
+
     assert_raise(ArgumentError){ Net::HTTP::Get.new(URI("urn:ietf:rfc:7231")) }
     assert_raise(ArgumentError){ Net::HTTP::Get.new(URI("http://")) }
   end
@@ -89,5 +101,25 @@ def test_header_set
                          'Bug #7831 - do not decode content if the user overrides'
   end if Net::HTTP::HAVE_ZLIB
 
+  def test_update_uri
+    req = Net::HTTP::Get.new(URI.parse("http://203.0.113.1"))
+    req.update_uri("test", 8080, false)
+    assert_equal "203.0.113.1", req.uri.host
+    assert_equal 8080, req.uri.port
+
+    req = Net::HTTP::Get.new(URI.parse("http://203.0.113.1:2020"))
+    req.update_uri("test", 8080, false)
+    assert_equal "203.0.113.1", req.uri.host
+    assert_equal 8080, req.uri.port
+
+    req = Net::HTTP::Get.new(URI.parse("http://[2001:db8::1]"))
+    req.update_uri("test", 8080, false)
+    assert_equal "[2001:db8::1]", req.uri.host
+    assert_equal 8080, req.uri.port
+
+    req = Net::HTTP::Get.new(URI.parse("http://[2001:db8::1]:2020"))
+    req.update_uri("test", 8080, false)
+    assert_equal "[2001:db8::1]", req.uri.host
+    assert_equal 8080, req.uri.port
+  end
 end
-