diff --git a/CHANGELOG.md b/CHANGELOG.md
index 58a4c0477..9f6589bba 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -10,7 +10,7 @@
 
 **Fixes and enhancements:**
 
-- Your contribution here
+- Fix rejection of unknown algorithms from JWKs for RFC compliance and pquip [#728](https://github.com/jwt/ruby-jwt/pull/728)
 
 ## [v3.2.0](https://github.com/jwt/ruby-jwt/tree/v3.2.0) (2026-05-13)
 
diff --git a/lib/jwt/error.rb b/lib/jwt/error.rb
index 2a0f8a2ce..ea4c9d71c 100644
--- a/lib/jwt/error.rb
+++ b/lib/jwt/error.rb
@@ -51,4 +51,7 @@ class Base64DecodeError < DecodeError; end
 
   # The JWKError class is raised when there is an error with the JSON Web Key (JWK).
   class JWKError < DecodeError; end
+
+  # Raised when a JWK uses a key type (kty) that this library does not support.
+  class UnsupportedKeyType < JWKError; end
 end
diff --git a/lib/jwt/jwk.rb b/lib/jwt/jwk.rb
index d717bac78..231029f9a 100644
--- a/lib/jwt/jwk.rb
+++ b/lib/jwt/jwk.rb
@@ -13,7 +13,7 @@ def create_from(key, params = nil, options = {})
           raise JWT::JWKError, 'Key type (kty) not provided' unless jwk_kty
 
           return mappings.fetch(jwk_kty.to_s) do |kty|
-            raise JWT::JWKError, "Key type #{kty} not supported"
+            raise JWT::UnsupportedKeyType, "Key type #{kty} not supported"
           end.new(key, params, options)
         end
 
diff --git a/lib/jwt/jwk/set.rb b/lib/jwt/jwk/set.rb
index 6f93e56ee..2a11aee57 100644
--- a/lib/jwt/jwk/set.rb
+++ b/lib/jwt/jwk/set.rb
@@ -22,7 +22,11 @@ def initialize(jwks = nil, options = {}) # rubocop:disable Metrics/CyclomaticCom
                   [jwks]
                 when Hash
                   jwks = jwks.transform_keys(&:to_sym)
-                  [*jwks[:keys]].map { |k| JWT::JWK.new(k, nil, options) }
+                  [*jwks[:keys]].each_with_object([]) do |k, arr|
+                    arr << JWT::JWK.new(k, nil, options)
+                  rescue JWT::UnsupportedKeyType
+                    nil
+                  end
                 when Array
                   jwks.map { |k| JWT::JWK.new(k, nil, options) }
                 else
diff --git a/spec/jwt/jwk/set_spec.rb b/spec/jwt/jwk/set_spec.rb
index 972f35fff..4678db08f 100644
--- a/spec/jwt/jwk/set_spec.rb
+++ b/spec/jwt/jwk/set_spec.rb
@@ -36,6 +36,38 @@
       end
     end
 
+    it 'ignores keys with unsupported kty values (RFC 7517 §5), required for hybrid PQC' do
+      jwks = {
+        keys: [
+          { kty: 'unknown', alg: 'unknown-alg', kid: 'unknown' },
+          { kty: 'oct', k: Base64.strict_encode64('testkey') }
+        ]
+      }
+      set = described_class.new(jwks)
+      expect(set.size).to eql(1)
+      expect(set.keys[0][:kty]).to eql('oct')
+    end
+
+    it 'returns an empty set when all keys have unsupported kty values' do
+      jwks = {
+        keys: [
+          { kty: 'unknown', alg: 'unknown-alg', kid: 'unknown-1' },
+          { kty: 'future', alg: 'future-alg', kid: 'future-1' }
+        ]
+      }
+      set = described_class.new(jwks)
+      expect(set.size).to eql(0)
+    end
+
+    it 'raises on malformed keys with a known kty' do
+      jwks = {
+        keys: [
+          { kty: 'RSA' }
+        ]
+      }
+      expect { described_class.new(jwks) }.to raise_error(JWT::JWKError, /Key format is invalid for RSA/)
+    end
+
     it 'raises an error on invalid inputs' do
       expect { described_class.new(42) }.to raise_error(ArgumentError)
     end