diff --git a/internal/sshproxy/server.go b/internal/sshproxy/server.go
index 9cde3f5..e52ce19 100644
--- a/internal/sshproxy/server.go
+++ b/internal/sshproxy/server.go
@@ -6,6 +6,7 @@ import (
 	"fmt"
 	"io"
 	"net"
+	"slices"
 	"strconv"
 	"strings"
 	"sync"
@@ -28,6 +29,20 @@ const (
 	upstreamDialTimeout          = time.Second * 10
 )
 
+var blacklistedGlobalRequests = []string{
+	// Host key update mechanism for SSH: https://www.ietf.org/archive/id/draft-miller-sshm-hostkey-update-02.html
+	// Reasons to blacklist:
+	// 1. Signature check always fail as the signed data contains session identifier, which is not the same on client
+	// and upstream side, since they don't talk directly but through sshproxy (there are two SSH transport sessions
+	// with their own unique identifiers).
+	// 2. Even if it worked somehow, we don't want to inflate user's known_hosts file with garbage records,
+	// since container host keys are ephemeral -- they are generated on dstack-runner startup (= unique for each job).
+	"hostkeys",
+	"hostkeys-00@openssh.com",
+	"hostkeys-prove",
+	"hostkeys-prove-00@openssh.com",
+}
+
 type direction string
 
 var (
@@ -386,15 +401,22 @@ func bridgeGlobalRequests(ctx context.Context, dir direction, inReqs <-chan *ssh
 	logger := log.GetLogger(ctx).WithField("dir", dir)
 	for req := range inReqs {
 		logger := logger.WithField("type", req.Type)
-		logger.Trace("global request")
 
-		reply, payload, err := outConn.SendRequest(req.Type, req.WantReply, req.Payload)
-		if req.WantReply {
-			_ = req.Reply(reply, payload)
-		}
+		if slices.Contains(blacklistedGlobalRequests, req.Type) {
+			logger.Trace("blacklisted global request, ignoring")
+			if req.WantReply {
+				_ = req.Reply(false, nil)
+			}
+		} else {
+			logger.Trace("global request")
+			ok, payload, err := outConn.SendRequest(req.Type, req.WantReply, req.Payload)
+			if req.WantReply {
+				_ = req.Reply(ok, payload)
+			}
 
-		if err != nil && !isClosedError(err) {
-			logger.WithError(err).Error("failed to forward global request")
+			if err != nil && !isClosedError(err) {
+				logger.WithError(err).Error("failed to forward global request")
+			}
 		}
 	}
 }
@@ -488,9 +510,9 @@ func bridgeChannelRequests(ctx context.Context, dir direction, inReqs <-chan *ss
 		logger := logger.WithField("type", req.Type)
 		logger.Trace("request")
 
-		reply, err := outConn.SendRequest(req.Type, req.WantReply, req.Payload)
+		ok, err := outConn.SendRequest(req.Type, req.WantReply, req.Payload)
 		if req.WantReply {
-			_ = req.Reply(reply, nil)
+			_ = req.Reply(ok, nil)
 		}
 
 		if err != nil && !isClosedError(err) {